Optical stress generator and detector

ABSTRACT

Disclosed is a system for the characterization of thin films and interfaces between thin films through measurements of their mechanical and thermal properties. In the system light is absorbed in a thin film or in a structure made up of several thin films, and the change in optical transmission or reflection is measured and analyzed. The change in reflection or transmission is used to give information about the ultrasonic waves that are produced in the structure. The information that is obtained from the use of the measurement methods and apparatus of this invention can include: (a) a determination of the thickness of thin films with a speed and accuracy that is improved compared to earlier methods; (b) a determination of the thermal, elastic, and optical properties of thin films; (c) a determination of the stress in thin films; and (d) a characterization of the properties of interfaces, including the presence of roughness and defects.

CLAIM OF PRIORITY FROM A COPENDING PROVISIONAL PATENT APPLICATION

This is a Division of U.S. patent application Ser. No. 09/511,719 filedon Feb. 23, 2000, which is a Divison of Ser. No. 09/382,251, filed onAug. 24, 1999, now U.S. Pat. No.: 6,175,416, issued on Jan. 16, 2001,which is a Divison of U.S. patent application Ser. No. 08/954,347, filedon Oct. 17, 1997, now U.S. Pat. No.: 5,959,735, issued on Sep. 28, 1999,which is a Divison of U.S. patent application Ser. No. 08/689,287, filedon Aug. 6, 1996, now U.S. Pat. No.: 5,748,318, issued on May 5, 1998,which claims priority under 35 U.S.C. §119(e) from Provisional PatentApplication No.: 60/010,543, filed on Jan. 23, 1996, in the names ofHumphrey Maris and Robert Stoner, and entitled “Improved Optical stressGenerator and Detector”, incorporated by reference herein in itsentirety.

STATEMENT OF GOVERNMENT RIGHTS

This invention was made with government support under grant/contractnumber DEFG02-ER45267 awarded by the Department of Energy. Thegovernment has certain rights in the invention.

FIELD OF THE INVENTION

This invention relates to a system for measuring the properties of thinfilms, and more particularly to a system which optically induces stresspulses in a film and which optically measures the stress pulsespropagating within the film.

BACKGROUND OF THE INVENTION

Presently, the nondestructive evaluation of thin films and interfaces isof interest to manufacturers of electrical, optical and mechanicaldevices which employ thin films In one nondestructive technique a radiofrequency pulse is applied to a piezoelectric transducer mounted on asubstrate between the transducer and the film to be studied. A stresspulse propagates through the substrate toward the film. At the boundarybetween the substrate and the film, part of the pulse is reflected backto the transducer. The remainder enters the film and is partiallyreflected at the opposite side to return through the substrate to th etransducer. The pulses are converted into electrical signals, amplifiedelectronically, and displayed on an oscilloscope. The time delay betweenthe two pulses indicates the film thickness, if the sound velocity inthe film is known, or indicates the sound velocity, if the filmthickness is known. Relative amplitudes of the pulses provideinformation on the attenuation in the film or the quality of the bondbetween the film and the substrate.

The minimum thickness of films which can be measured and the sensitivityto film interface conditions using conventional ultrasonics is limitedby the pulse length. The duration of the stress pulse is normally atleast 0.1 μsec corresponding to a spatial length of at least 3×10⁻² cmfor an acoustic velocity of 3×10⁵ cm/sec. Unless the film is thickerthan the length of the acoustic pulse, the pulses returning to thetransducer will overlap in time. Even if pulses as short in duration as0.001 μsec are used, the film thickness must be at least a few microns.

Another technique, acoustic microscopy, projects sound through a rodhaving a spherical lens at its tip. The tip is immersed in a liquidcovering the film. Sound propagates through the liquid, reflects off thesurface of the sample, and returns through the rod to the transducer.The amplitude of the signal returning to the transducer is measuredwhile the sample is moved horizontally. The amplitudes are converted toa computer-generated photograph of the sample surface. Sample featuresbelow the surface are observed by raising the sample to bring the focalpoint beneath the surface. The lateral and vertical resolution of theacoustic microscope are approximately equal.

Resolution is greatest for the acoustic microscope when a very shortwavelength is passed through the coupling liquid. This requires a liquidwith a low sound velocity, such as liquid helium. An acoustic microscopeusing liquid helium can resolve surface features as small as 500Angstroms, but only when the sample is cooled to 0.1 K.

Several additional techniques, not involving generation and detection ofstress pulses, are available for measuring film thickness. Ellipsometersdirect elliptically polarized light at a film sample and analyze thepolarization state of the reflected light to determine film thicknesswith an accuracy of 3-10 Angstroms. The elliptically polarized light isresolved into two components having separate polarization orientationsand a relative phase shift. Changes in polarization state, beamamplitudes, and phase of the two polarization components are observedafter reflection.

The ellipsometer technique employs films which are reasonablytransparent. Typically, at least 10% of the polarized radiation mustpass through the film. The thickness of metal sample films thus cannotexceed a few hundred Angstroms.

Another technique uses a small stylus to mechanically measure filmthickness. The stylus is moved across the surface of a substrate and,upon reaching the edge of a sample film, measures the difference inheight between the substrate and the film. Accuracies of 10-100Angstroms can be obtained. This method cannot be used if the film lacksa sharp, distinct edge, or is too soft in consistency to accuratelysupport the stylus.

Another non-destructive method, based on Rutherford Scattering, measuresthe energy of backscattered helium ions. The lateral resolution of thismethod is poor.

Yet another technique uses resistance measurements to determine filmthickness. For a material of known resistivity, the film thickness isdetermined by measuring the electrical resistance of the film. For filmsless than 1000 Angstroms, however, this method is of limited accuracybecause the resistivity may be non-uniformly dependent on the filmthickness.

In yet another technique, the change in the direction of a reflectedlight beam off a surface is studied when a stress pulse arrives at thesurface. In a particular application, stress pulses are generated by apiezoelectric transducer on one side of a film to be studied. A laserbeam focused onto the other side detects the stress pulses after theytraverse the sample. This method is useful for film thicknesses greaterthan 10 microns.

A film may also be examined by striking a surface of the film with anintense optical pump beam to disrupt the film's surface. Rather thanobserve propagation of stress pulses, however, this method observesdestructive excitation of the surface. The disruption, such as thermalmelting, is observed by illuminating the site of impingement of the pumpbeam with an optical probe beam and measuring changes in intensity ofthe probe beam. The probe beam's intensity is altered by suchdestructive, disruptive effects as boiling of the film's surface,ejection of molten material, and subsequent cooling of the surface.

See Downer, M. C.; Fork, R. L.; and Shank, C. V., “Imaging withFemtosecond Optical Pulses”, Ultrafast Phenomena IV, Ed. D. H. Austonand K. B. Eisenthal (Spinger-Verlag, N.Y. 1984), pp. 106-110.

Other systems measure thickness, composition or concentration ofmaterial by measuring absorption of suitably-chosen wavelengths ofradiation. This method is generally applicable only if the film is on atransparent substrate.

In a nondestructive ultrasonic technique described in U.S. Pat. No.4,710,030 (Tauc et al.), a very high frequency sound pulse is generatedand detected by means of an ultrafast laser pulse. The sound pulse isused to probe an interface. The ultrasonic frequencies used in thistechnique typically are less than 1 THz, and the corresponding sonicwavelengths in typical materials are greater than several hundredAngstroms. It is equivalent to refer to the high frequency ultrasonicpulses generated in this technique as coherent longitudinal acousticphonons.

In more detail, Tauc et al. teach the use of pump and probe beams havingdurations of 0.01 to 100 psec. These beams may impinge at the samelocation on a sample's surface, or the point of impingement of the probebeam may be shifted relative to the point of impingement of the pumpbeam. In one embodiment the film being measured can be translated inrelation to the pump and probe beams. The probe beam may be transmittedor reflected by the sample. In a method taught by Tauc et al. the pumppulse has at least one wavelength for non-destructively generating astress pulse in the sample. The probe pulse is guided to the sample tointercept the stress pulse, and the method further detects a change inoptical constants induced by the stress pulse by measuring an intensityof the probe beam after it intercepts the stress pulse.

In one embodiment a distance between a mirror and a corner cube isvaried to vary the delay between the impingement of the pump beam andthe probe beam on the sample. In a further embodiment anopto-acoustically inactive film is studied by using an overlying filmcomprised of an opto-acoustically active medium, such as arsenictelluride. In another embodiment the quality of the bonding between afilm and the substrate can be determined from a measurement of thereflection coefficient of the stress pulse at the boundary, andcomparing the measured value to a theoretical value.

The methods and apparatus of Tauc et al. are not limited to simplefilms, but can be extended to obtaining information about layerthicknesses and interfaces in superlattices, multilayer thin-filmstructures, and other inhomogeneous films. Tauc et al. also provide forscanning the pump and probe beams over an area of the sample, as smallas 1 micron by 1 micron, and plotting the change in intensity of thereflected or transmitted probe beam.

While well-suited for use in many measurement applications, it is anobject of this invention to extend and enhance the teachings of Tauc etal.

OBJECTS OF THE INVENTION

It is thus an object of this invention to provide an improved opticalgenerator and detector of stress pulses.

It is a further object of this invention to provide an improvedultrafast optical technique for measuring stress in a thin film.

It is still another object of this invention to provide an improvedultrafast optical technique for determining the elastic modulus, soundvelocity, and refractive index of a thin film.

It is a still further object of this invention to provide an improvedultrafast optical technique for characterizing an interface between twomaterials, such as an interface between a substrate and an overlyingthin film.

It is another object of this invention to provide an ultrafast opticaltechnique for determining a derivative of a transient response of asample to a pump pulse, and for correlating the derivative with acharacteristic of interest, such as the static stress within the sample.

It is another object of this invention to provide an ultrafast opticaltechnique for varying a temperature of the sample and, while varying thetemperature, for determining a derivative of the acoustic velocitywithin the sample and for subsequently correlating the derivative of theacoustic velocity with the static stress within the sample.

It is another object of this invention to provide an ultrafast opticaltechnique for determining an electrical resistivity of a sample.

It is a further object of this invention to provide simulation methodsfor modelling a time-evolved effect of a stress pulse generated within asample of interest, and to then employ the model to characterize thesample.

It is a further object of this invention to provide an ultrafast opticaltechnique for measuring a characteristic of interest in a patterned,periodic, multilayered structure.

It is one still further object of this invention to provide an ultrafastoptical system and technique wherein optical fibers are used toadvantage for directing and/or focussing at least one of an incidentpump beam, and incident probe beam, or a reflected or transmitted probebeam.

It is another object of this invention to provide a non-destructivesystem and method for simultaneously measuring at least two transientresponses of a structure to a pump pulse, the measured transientresponses comprising at least two of a measurement of a modulated changeΔR in an intensity of a reflected portion of a probe pulse, a change ΔTin an intensity of a transmitted portion of the probe pulse, a change ΔPin a polarization of the reflected probe pulse, a change ΔΦ in anoptical phase of the reflected probe pulse, and a change in an angle ofreflection Δβ of the probe pulse.

It is one further object of this invention to provide a non-destructivesystem and method for determining a characteristic of a sample thatincludes an automatic control over the focussing of pump and probe beamsat the sample so as to provide a reproducible intensity variation of thebeams during each measurement.

SUMMARY OF THE INVENTION

The foregoing and other problems are overcome and the objects of theinvention are realized by methods and apparatus in accordance withembodiments of this invention.

This invention relates to a system for the characterization of thinfilms and interfaces between thin films through measurements of theirmechanical, optical, and thermal properties. In the system of thisinvention incident light is absorbed in a thin film or in a structuremade up of several thin films, and the change in optical transmission orreflection is measured and analyzed. The change in reflection ortransmission is used to give information about the ultrasonic waves thatare produced in the structure. The information that is obtained from theuse of the measurement methods and apparatus of this invention caninclude: (a) a determination of the thickness of thin films with a speedand accuracy that is improved compared to earlier methods; (b) adetermination of the thermal, elastic, electrical, and opticalproperties of thin films; (c) a determination of the stress in thinfilms; and (d) a characterization of the properties of interfaces,including the presence of roughness and defects.

The invention features a radiation source for providing a pump beam anda detection system for non-destructively measuring the properties of oneor more interfaces within a sample. The radiation source provides thepump beam so as to have short duration radiation pulses having anintensity and at least one wavelength selected to non-destructivelyinduce a propagating stress wave in the sample, a radiation source forproviding a probe beam, a mechanism for directing the pump beam to thesample to generate the stress wave within the sample, and a mechanismfor guiding the probe beam to a location at the sample to intercept thestress wave. A suitable optical detector is provided that is responsiveto a reflected or transmitted portion of the probe beam for detecting achange in the optical constants of the material induced by the stresswave.

In one embodiment, the optical detector measures the intensity of thereflected or transmitted probe beam. The pump and probe beam may bederived from the same source that generates a plurality of shortduration pulses, and the system further includes a beam splitter fordirecting a first portion of the source beam to form the pump beam,having the plurality of pulses, and directing a second portion to formthe probe beam, also having the plurality of pulses. The source beam hasa single direction of polarization and the system further includes meansfor rotating the polarization of the probe beam and a device, disposedbetween a sample and the optical detector, for transmitting onlyradiation having the rotated direction of polarization. The system mayfurther include a temperature detector and a chopper for modulating thepump beam at a predetermined frequency. The system can further include amechanism for establishing a predetermined time delay between theimpingement of a pulse of the pump beam and a pulse of the probe beamupon the sample. The system can further include circuitry for averagingthe output of the optical detector for a plurality of pulse detectionswhile the delay between impingements remains set at the predeterminedtime delay. The delay setting mechanism may sequentially change thepredetermined time delay and the circuitry for averaging maysuccessively average the output of the optical detector during eachsuccessive predetermined time delay setting.

By example, the pump beam may receive 1% to 99% of the source beam, andthe source beam may have an average power of 10 μW to 10 kW. The sourcebeam may include wavelengths from 100 Angstroms to 100 microns, and theradiation pulses of the source beam may have a duration of 0.01 psec to100 psec.

The sample may include a substrate and at least one thin film to beexamined disposed on the substrate such that interfaces exist where thefilms meet, and/or where the film and the substrate meet. For a samplewith an optically opaque substrate, at the pump wavelength, the pump andprobe beams may both impinge from the film side, or the pump may impingefrom the film side and the probe may impinge from the substrate side.For a sample with a transparent substrate, both beams may impinge fromthe film side, or from the substrate side, or from opposite sides of thesample. The optical and thermal properties are such that the pump pulsechanges the temperature within at least one film with respect to thesubstrate. The temperature within one or more of the thin films disposedon the substrate may be uniform, and may be equal in several films. Thefilms may have thicknesses ranging from 1 Å to 100 microns. At least onefilm in the sample and/or the substrate has the property that when astress wave is present it causes a change in the intensity, opticalphase, polarization state, position, or direction of the probe beam atthe detector. The probe beam source may provide a continuous radiationbeam, and the pump beam source may provide at least one discrete pumppulse having a duration of 0.01 to 100 psec and an average power of 10μW to 1 kW. Alternatively the probe beam source may provide probe beampulses having a duration of 0.01 to 100 psec, the pump beam and probebeam may impinge at the same location on the sample, and the mechanismsfor directing and guiding may include a common lens system for focusingthe pump beam and the probe beam onto the sample. The position ofimpingement of the probe beam may be shifted spatially relative to thatof the pump beam, and the probe beam may be transmitted or reflected bythe sample.

One or more fiber optic elements may be incorporated within the system.Such fibers may used to guide one or more beams within the system forreducing the size of the system, and/or to achieve a desired opticaleffect such as focussing of one or more beams onto the surface of thesample. To achieve focussing, the fiber may be tapered, or mayincorporate a small lens at its output. A similar focussing fiber can beused to gather reflected probe light and direct it to an opticaldetector. A fiber may also be used to modify the beam profile, or as aspatial filter to effect a constant beam profile under widely varyinginput beam conditions.

This invention advantageously provides a non-destructive system andmethod for measuring at least one transient response of a structure to apump pulse of optical radiation, the measured transient response orresponses including at least one of a measurement of a modulated changeΔR in an intensity of a reflected portion of a probe pulse, a change ΔTin an intensity of a transmitted portion of the probe pulse, a change ΔPin a polarization of the reflected probe pulse, a change ΔΦ in anoptical phase of the reflected probe pulse, and a change in an angle ofreflection A6 of the probe pulse, each of which may be considered as achange in a characteristic of a reflected or transmitted portion of theprobe pulse. The measured transient response or responses are thenassociated with at least one characteristic of interest of thestructure.

In a presently preferred embodiment the system provides forautomatically focusing the pump and probe pulses to achievepredetermined focusing conditions, and the application of at least onecalibration factor to the at least one transient response. Thisembodiment is especially useful when employed with time-evolvedsimulations and models of a structure of interest, which is a furtheraspect of this invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The above set forth and other features of the invention are made moreapparent in the ensuing Detailed Description of the Invention when readin conjunction with the attached Drawings, wherein:

FIGS. 1a-1 c depict embodiments of optical sources for use with thesystem of this invention;

FIG. 2 is a block diagram of an embodiment of a sample characterizationsystem in accordance with this invention;

FIGS. 3a-3 f each depict an embodiment of a pump beam/probe beamdelivery technique to a surface of a sample;

FIG. 4a is a diagram that illustrates a variability in a temporal offsetbetween pump and probe beam pulses;

FIG. 4b is block diagram that illustrates an embodiment ofelectro-optical components responsive to the delay between the pump andprobe pulses, as shown in FIG. 4a;

FIG. 5 is a cross-sectional, enlarged view of a sample having asubstrate, a thin film layer, and an interface between the substrate andthe thin film layer, and that further illustrates a stress-induceddeformation in the thin film wherein constructive and destructive probebeam interference occurs;

FIG. 6 illustrates a second embodiment of the interface characterizationsystem in accordance with this invention;

FIG. 7 illustrates a fiber optic-based pump and probe beam delivery andfocussing system in accordance with an embodiment of this invention;

FIG. 8 illustrates a further embodiment of this invention wherein alength of fiber optic is employed to compensate for a change in probebeam profile as a function of delay between the pump and probe beampulses;

FIG. 9 illustrates an embodiment of a delay stage used for setting adelay between the pump and probe beam pulses;

FIG. 10 is a cross-sectional, enlarged view of the sample having thesubstrate, thin film layer, and the interface between the substrate andthe thin film layer, and that further illustrates the impingement of theprobe beam within a focussed spot (FS1) of the pump beam, and theimpingement of the probe beam at a second FS (FS2) that is displacedfrom FS1;

FIG. 11 is an enlarged, cross-sectional view of a silicon-on-insulator(SOI) sample that is amenable to characterization in accordance withthis invention;

FIG. 12 is a cross-sectional, enlarged view of the sample having thesubstrate, a localized thin film structure disposed on a surface of thesubstrate, and the interface between the substrate and the thin filmstructure, and that further illustrates various methods to apply thepump and probe beams;

FIG. 13 is a cross-sectional, enlarged view of the sample having thesubstrate, a localized thin film structure disposed within a surface ofthe substrate, and the interface between the substrate and the thin filmstructure, and that further illustrates various methods to apply thepump and probe beams;

FIG. 14 is a cross-sectional, enlarged view of a sample having asubstrate, a plurality of thin film layers, and interfaces between thesubstrate and one of the thin film layers and between the thin filmlayers;

FIGS. 15a-15 d each illustrate an optically-induced stress wave, havinga velocity v_(s), that propagates in a material, and the reflection of aportion of the probe beam from the stress wave;

FIG. 16 a block diagram of a first embodiment of a picosecond ultrasonicsystem in accordance with this invention, specifically, a parallel,oblique beam embodiment;

FIG. 17 is a block diagram of a second embodiment of a picosecondultrasonic system in accordance with this invention, specifically, anormal pump, oblique probe embodiment;

FIG. 18 is a block diagram of a third, presently preferred embodiment ofa picosecond ultrasonic system in accordance with this invention,specifically, a single wavelength, normal pump, oblique probe, combinedellipsometer embodiment;

FIG. 19 is a block diagram of a fourth embodiment of a picosecondultrasonic system in accordance with this invention, specifically, adual wavelength, normal pump, oblique probe, combined ellipsometerembodiment;

FIG. 20 is a block diagram of a fifth embodiment of a picosecondultrasonic system in accordance with this invention, specifically, adual wavelength, normal incidence pump and probe, combined ellipsometerembodiment; and

FIG. 21 is a logic flow diagram that illustrates a simulation method inaccordance with an aspect of this invention.

DETAILED DESCRIPTION OF THE INVENTION

The disclosure of the above-referenced U.S. Pat. No. 4,710,030 (Tauc etal.) is incorporated by reference herein in its entirety.

The teaching of this invention is embodied by an optical generator anddetector of a stress wave within a sample. In this system a firstnon-destructive pulsed beam of electromagnetic radiation is directedupon a sample containing at least one film and possibly also aninterface between similar or dissimilar materials. The first pulsed beamof electromagnetic radiation, referred to herein as a pump beam 21 a,produces a propagating stress wave within the sample. A secondnon-destructive pulsed beam of electromagnetic radiation, referred toherein as a probe beam 21 b, is directed upon the sample such that atleast one of the polarization, optical phase, position, direction andintensity of a reflected portion of the probe beam 21 b′ or atransmitted portion of the probe beam 21 b″ is affected by a change inthe optical constants of the materials comprising the sample, or by achange in the thickness of one or more layers or sublayers within a thinfilm sample due to a propagating stress wave. Physical and chemicalproperties of the materials, and possibly also of the interface, aremeasured by observing the changes in the reflected or transmitted probebeam intensity, direction, or state of polarization as revealed by thetime dependence of the changes in beam intensity, direction or state ofpolarization. The very short time scale is particularly important forachieving a high sensitivity to interfacial and other properties, andfor measuring the properties of films having thicknesses less thanseveral microns.

By way of introduction, the arrangement of the pump and probe beamaccording to this invention is illustrated in FIG. 10. A test sample 51is shown comprised of a film 84 disposed on substrate 80. An interface82 is formed between the film 84 and the substrate 80. By example, thesubstrate 80 may be comprised of a semiconductor such as silicon and mayform a portion of a semiconductor wafer, and the film 84 may be anoverlying layer of oxide, polymer, metal, or another semiconductor. Inanother exemplary embodiment the sample may be a SOI wafer comprised ofa silicon substrate, a thin layer of silicon oxide, and an overlying(typically thin) layer of silicon, as is shown in FIG. 11. To test thesample 51 the pump beam 21 a is directed onto a position on the film 84(referred to as a focal spot FS1) to generate a stress wave in thesample due to the absorption of energy in the film 84 or substrate 80.The pump beam 21 a is incident on the sample 51 at an angle θ₁ offsetfrom normal. The unabsorbed portion of the pump beam is reflected as thereflected pump beam 21 a′. The probe beam 21 b may be directed to thesame spot (FS1) on the sample at an angle θ₂ to intercept the stresspulse generated by the pump beam 21 a. In other embodiments of theinvention the probe beam 21 b can be directed to another location (FS2).A portion of the probe beam 21 b reflects from the film 84 as thereflected probe beam 21 b′. Any portion of the probe beam 21 b that istransmitted through the sample is referred to as the transmitted probebeam 21 b″. The actual values of angles θ₁ and θ₂ can be selected from awide range of angles. The intensities of the reflected and transmittedpump and probe beams depend on the optical constants of the film 84 andsubstrate 80 and on the thicknesses of the films.

FIG. 10 also illustrates probing at points (FS2) at a distance from thepump beam FS1, which applies to the ultrasonic and all otherapplications disclosed herein.

For a sufficiently thick opaque film disposed on a substrate the pumplight will be absorbed in a surface layer of thickness small compared tothe film thickness. The absorption in the surface layer generates astress pulse which propagates back and forth in the film, giving rise toa series of equally-separated features (“echoes”) in the responsesmeasured by the probe beam. The thickness of a simple film that is thickenough to have distinct echoes can be determined from the echo time, asdescribed by Tauc et al. For a thinner film, the echoes become soclosely spaced that they degenerate into vibrational thickness modes ofthe film, appearing as damped oscillations in the data, and thethickness can be deduced from the vibration period. For intermediatethickness films, or for films composed of multiple layers, the data maybe too complicated to analyze so simply. In such cases it is preferredto construct a theoretical model for the vibrating structure in whichthere may be one or more adjustable unknowns (e.g. film thicknesses,densities, sound velocities). The theoretical model is used to simulatethe vibrations of the structure over a suitable time interval (indiscrete time steps), and to calculate the corresponding change in theoptical reflectivity of the sample (or transmission, or polarizationstate, or optical phase of the transmitted or reflected beams caused bythe stress induced change in the optical constants of the sample, or bystress induced displacements of the surface or of interfaces within thestructure). The duration of the time steps are preferably selected to besmall compared to a time required for an acoustic wave to propagatethrough a thinnest layer of the structure (e.g., 0.1 psec to 200 psec).By example, the duration of each time step can be established at lessthan one half (e.g., one tenth) of the propagation time through thethinnest layer. Also by example, the duration of each time step can beselected to be small compared to a shortest absorption length(penetration depth) for the pump or probe light in the structure.

A method for finding any number of unknowns is to compute a simulatedoptical response for a particular set of parameters, and then to adjustthe values of the parameters as needed to achieve a best-fit to themeasured result. Presently preferred methods for carrying out thismodelling and simulation are described in detail below with reference toFIG. 21.

The basic equations for the vibrational part of the simulations aretaken from well-known continuum elasticity theory. The basic equationsfor the optical part of the simulation are the Fresnel equations. As anillustration in one dimension (i.e. for a sample 51 with a stress wavepropagating with velocity v_(s) along a direction z normal to thesurface), the quantity to be computed in the simulation can be writtenas follows: $\begin{matrix}{{\Delta \quad {R(t)}} = {\int_{0}^{\infty}{{f(z)}{\eta_{33}( {z,t} )}\quad {z}}}} & (1)\end{matrix}$

In this equation f(z) is the change in the reflectivity with strainassociated with stress η₃₃(z,t) at depth z. ΔR(t) is the strain inducedchange in the optical reflectivity of the sample at a time t. Similarequations can be written for changes in the transmission or in thepolarization state of the probe beam 21 b. The function f(z) includesthe effect of strain on the optical constants within the sample 51, aswell as the effect of displacement of the surface or internal interfaces(i.e. a time-dependent change in the thickness of one or more layers)due to the presence of a stress wave.

In accordance with an aspect of this invention, the physical propertiesof the sample 51 which may be determined in this way include propertieswhich may affect the time dependence of ultrasonic signals, and/or theiramplitudes. These are (among others) layer thicknesses, soundvelocities, interfacial roughness, interfacial adhesion strength,thermal diffusivities, stress, strain, optical constants, surfaceroughness, and interfacial contaminants.

FIGS. 1a-1 c illustrate various embodiments of optical sources that aresuitable for practicing this invention, while FIG. 2 is a block diagramof an optical generation and detection system for performingnon-destructive picosecond time-scale thin film and interfacecharacterizations, referred to hereinafter as sample 1.

A first embodiment of an optical source 10 is shown in FIG. 1a, in whichthe beam from a laser 12 is reflected from a mirror 14 and passesthrough a polarization rotating device, such as a half-wave plate 16, toa polarizing beam splitter 18. The beams emerging from the polarizingbeam splitter 18 are orthogonally polarized, and the ratio of theirintensities may be varied through a wide range by adjusting theorientation of the half-wave plate 16. One beam forms the pump beam 21a, while the probe beam 21 b reflects from a mirror 20.

An alternative embodiment of an optical source 10′ shown in FIG. 1bincludes a frequency doubling crystal 24, such as BBO or LBO, onto whichthe laser light is focused by a lens 22 positioned between it and thelaser 12. The coaxial beams of light emerging from the frequencydoubling crystal 24 are separated by means of a dichroic mirror 26 intothe pump and probe beams, each of which is then collimated by lenses 28and 30. The polarization of the pump beam 21 a is rotated to beperpendicular to that of the probe beam 21 b by means of a half-waveplate 32. The dichroic mirror 26 may be chosen to pass the fundamentalfrequency of the laser 12 and reflect the second harmonic, giving aprobe beam at the fundamental and a pump beam at the second harmonic.Alternatively, the dichroic mirror 26 may be chosen to pass the secondharmonic and reflect the fundamental, giving the probe beam 21 b at thesecond harmonic and the pump beam 21 a at the fundamental, as shown inFIG. 1b.

Another embodiment of an optical source 10′ is shown in FIG. 1c, inwhich the pump and probe beams are produced by two different lasers 12and 13. In one embodiment, these may be identical pulsed lasers, inwhich case the upper beam is passed through the half-wave plate 16 torotate its polarization relative to that of the lower beam by 90degrees. Alternatively, the lasers 12 and 13 may emit dissimilarwavelengths (two “colors”). Alternatively, the probe laser 13 may emit acontinuous (i.e. non-pulsed) beam. Alternatively, the pump laser 12 mayemit pulses with a repetition period of τ_(A) and the probe laser 13 mayemit pulses with a repetition period τ_(B), as shown in FIG. 4a. Such ascheme may be used to effect a continuously variable delay between thepump and probe pulses without the use of a mechanical delay stage 44 ofa type depicted in FIG. 2.

Referring now to FIG. 4b, in this alternative technique the delaybetween pairs of A and B pulses increases by a time τ_(B)-τ_(A) from onerepetition to the next. By example, τ_(B)-τ_(A) may be 0.1 psec onaverage, and the repetition rate of the pump laser 12 may be 100 MHz.This gives a time between simultaneous arrivals of the pump and probepulses of one millisecond (i.e., the scan time). This embodiment furtherincludes suitable frequency locking electronics (FLE), mirrors, a lens,a suitable detector 60, and a fast signal averager (SA). A measurementof, by example, ΔR(t) may be performed by applying a signalcorresponding to the reflected probe intensity from the output of thedetector 60 to the input of the fast signal averager (SA), and bytriggering sample acquisitions at times corresponding to the pulsing ofthe probe laser 13. A large number (e.g., thousands) of measurements maybe averaged in order to effect a desired signal to noise ratio. Itshould be noted in regard to this invention that the delay stage andmodulator described previously in regard to FIG. 2 may be omitted. Itshould also be appreciated that any “jitter” in the pulsing of the twolasers may have the effect of averaging the signals corresponding toclosely spaced delay times, and that this effect may somewhat attenuatethe high frequency components of the measurement.

Although the pump and probe lasers are depicted in FIG. 1c separately,they may have one or more optical elements in common, including the gainmedium. Other permutations of pump and probe color, polarization andpulse rate suggested by the above description may be used to achieve animprovement in signal quality, depending on the properties of thematerials to be investigated.

Examples of the pulsed lasers suitable for use in the system 1 includean Argon ion pumped solid state mode-locked laser, such as Coherent Inc.Inova (Argon) and Mira (Ti:sapphire); a diode laser pumped solid statemode locked laser, such as a continuous wave diode pumped frequencydoubled YAG and modelocked Ti:sapphire laser; and a direct diode pumpedmode-locked solid state laser.

Referring to the embodiment of FIG. 2, a further embodiment of anoptical source 10′″ provides both the pump and probe beams 21 a and 21b, respectively, in a manner similar to the embodiment of FIG. 1a. Inthe FIG. 2 arrangement the linearly polarized beam from laser 12 passesthrough the half-wave plate 16, which is used to rotate itspolarization. The polarized beam is then split into pump and probe beamsby a dielectric beam splitter 34. The ratio of pump to probe may bevaried by rotating the incoming polarization. The lower beam is the pumpbeam 21 a, and the upper beam is the probe beam 21 b. The pump beam 21 apasses through a half-wave plate/polarizer combination 38 which rotatesits polarization to be orthogonal to that of the probe beam 21 b, andwhich also suppresses any light not polarized along this orthogonalaxis.

The pump and probe beams 21 a and 21 b are emitted by the source, andthe intensity of the pump beam is modulated at a rate of about 1 MHz byan acousto-optic modulator (AOM) 40, or by a photoelastic modulatorfollowed by a polarizer, or by other intensity modulation means. Theprobe beam path length is varied by translating a retroreflector 46mounted on a computer-controlled delay stage 44, via a steering mirrorcombination 110 a. Both beams are then focused by lens 48 onto thesample 51 mounted on a translatable sample stage 50, and are detected bya photodetector 60. In this embodiment the inputs to the detector 60include portions of the input pump and probe beams (inputs c and b,respectively, via beam splitters 49 a and 49 b, respectively); and alsoinclude portions of the reflected pump beam 21 a′ and reflected probebeam 21 b′ (inputs d and a, respectively). Outputs from the detector 60include signals proportional to the incident pump beam intensity (e);incident probe beam intensity (f); reflected pump beam intensity (g);reflected probe beam intensity (h); and probe modulation intensity (i),i.e. only the modulated part of the reflected probe intensity. Thesedetector outputs are fed into a processor 66. The processor 66calculates from the inputs the fractional change in the sample'sreflectivity R (i.e. ΔR/R), and normalizes this change by the intensityof the incident pump beam.

In the apparatus of this invention the detector input designated as (a)contains a modulated component which carries the stress information inaddition to a large unmodulated reflected probe component 21 b′. Input(b) is proportional to the unmodulated portion of the probe signal 21 b.The output (i) is a voltage proportional to only the modulated part ofthe probe signal, which is determined by electronically removing theunmodulated component from the input (a). This output goes to a bandpassfilter and preamplifier 62, then to a synchronous demodulator 64 (e.g. alockin amplifier), and finally to the processor 66 where it is digitizedand stored. The inputs (a) and (b) are also used to determine thereflectivity of the sample corresponding to the probe beam 21 b, andsimilarly inputs (d) and (c) are used to determine the reflectivity ofthe sample corresponding to the pump beam 21 a. These quantities may beused to validate the optical simulation of the structure, or in somecases to deduce layer properties such as thickness in accordance withknown optical reflectometry principles. In addition, inputs (a) and (d)are used by the processor 66 to normalize the reflectivity change output(i). The energy deposited in the sample 51 by the pump beam 21 a may bedetermined by comparing the incident and reflected pump and probe beamintensities (21 a′, 21 b′).

Portions of the pump and probe beams may also be directed via beamsplitter 54 onto one or more position sensitive detectors (autofocusdetector 58) whose output may be used by the processor 66, inconjunction with the sample translation stage 50, to effect an optimumfocus of the pump and probe beams on the sample 51. The signal to noiseratio may be improved by placing color filters and/or polarizers betweenthe sample 51 and detector 60 to prevent light scattered from otherparts of the system from impinging one or more detectors (as an example,to prevent pump light scattered from the sample 51 from impinging onreflected probe intensity detector (a)). The signal quality may befurther improved by passing the modulated probe intensity output (i)from the detector 60 through the synchronous demodulator 64 (such as alockin amplifier, or signal averager) located before the processor 66.The signal quality may be further improved for samples 51 tending toscatter the pump beam 21 a into the probe detector by introducing asecond intensity modulator into the probe beam path between the source10 and the sample 51. The second intensity modulator has a modulationfrequency differing from the pump beam modulation frequency by an amountsuch that the difference frequency is greater than the input bandwidthof the synchronous demodulator 62. The detector output (i) correspondingto the reflected probe intensity may then be synchronously demodulatedat the difference frequency, while the components of (i) at themodulation frequencies are rejected.

The pump and probe beams may be focused, as in FIG. 2, onto the samplethrough the common lens 48. This arrangement is simple to practice butis not optimal for all cases, since the pump beam 21 a need be scatteredthrough only a small angle by a non-ideal sample to impinge on thereflected probe detector (a), thereby introducing noise to themeasurement of the modulated probe intensity. The common lens approachalso has the weakness of achieving non-optimal spot overlap, which maybe improved by using separate lenses, or coaxial beams. The common lensapproach is represented in FIG. 3d in plan view from a location along anormal to the sample, here a semiconductor wafer 70. Other focusinggeometries may give improved signal quality, depending on the propertiesof the sample (e.g. the amount of surface roughness), and the source(e.g. pump and probe beams having different colors, versus pump andprobe beams having the same color).

Alternative focusing geometries are also illustrated in FIG. 3, andinclude:

(FIG. 3a) pump and probe beams oblique to the sample plane (i.e., thesurface of wafer 70) and not parallel or coaxial to each other;

(FIG. 3b) pump and probe beams substantially normal to the sample planeand parallel, focused through a common lens 98 (as in FIG. 6);

(FIG. 3c) pump and probe beams parallel and lying in a plane orthogonalto the plane of incidence, focused through common lenses 48 and 52;

(FIG. 3e) (i) pump beam normal and probe beam oblique, focusedindependently; or (ii) probe normal and pump oblique; and

(FIG. 3f) pump beam and probe beam both normal to the sample plane andcoaxial, focused through a common lens 74.

The variable delay between the pump and probe beams may be implementedas shown in FIG. 2 by means of the computer controlled delay stage 44 inthe probe beam path. Alternatively, a similar delay stage may beinserted within the pump beam path to “advance” the pump beam pulses intime relative to the probe pulses. An extremely long delay may beimplemented as shown in FIG. 9 by placing more than one retroreflector46 on the single translation stage 44. In this embodiment a plurality ofthe beam steering mirrors 110 a are employed to direct the probe beam 21b to individual ones of the retroreflectors 46, thereby significantlyincreasing the probe beam path length relative to the pump beam pathlength. It is possible to implement a delay which is longer than thetime between successive pulses such that the effects of a pump pulsearriving at the sample more than one pulse interval before the probe maybe detected.

The shape and position of the focused probe spot FS on the surface ofthe sample 51 may vary systematically, depending on the position of thedelay stage 44 (i.e. the time delay). For example, the system 1 mayexhibit a lack of parallelism between the probe path in FIG. 2 and thedelay stage axis due to misalignment, or as a result of a flaw in thestage mechanism. This causes a translation of the probe beam across thefocusing lens, and for a lens exhibiting typical aberrations, canintroduce a corresponding lateral translation of the probe beam 21 brelative to the pump beam 21 a on the surface of the sample 51, as afunction of delay.

In addition, since all laser beams exhibit some degree of divergence,varying the path length of one of the beams changes its diameter at thefocusing lens, and this causes a corresponding change in the diameter ofthe focused spot (FS) on the sample 51. The result of all such effectsmay be to introduce a spurious dependence of the signal upon delay time.One method to eliminate such dependencies is shown in FIG. 8, in which alength of optical fiber 114 is introduced to the path of the delayedprobe beam (or advanced pump beam). The fiber 114 serves as a spatialfilter, preserving a constant spot position, size and profile throughouta range of input beam conditions. By incorporating such a device intothe probe beam path it is possible to preserve a very stable overlap ofthe pump and probe beams on the focus spot FS over a wide range of delaystage positions. Other types of spatial filters may also be used toachieve the same effect; for example, any small aperture (typicallysmaller than the beam size) such as a pinhole or narrow slit, followedby a second aperture so chosen as to block high spatial Fouriercomponents of the beam may be used. A lens may be used to focus the beamonto the first aperture, and a second lens may be used to collimate thebeam emerging from the second aperture. In a system employing any of theabove techniques it is preferred to monitor the intensity of the delayed(or advanced) beam either before or after it impinges on the sample, toproperly normalize the final signal.

Referring now to FIG. 5, there is illustrated a deflection through anangle θ of the probe beam 21 b by a non-uniform expansion of a regionwherein a propagating stress wave exists (i.e. a bulge 86 in the film84). The bulge 86 is caused at least in part by a stress wave which mayalso have a non-uniform profile across the spot. The deflection can bedetected by a position sensitive detector such as a split cell 60′.Movement of the reflected probe beam 21 b′ can also come about in theabsence of the bulge 86 in transparent and semi-transparent samples dueto a stress induced change in the refractive index. In this case thebeam is displaced by a small amount parallel to the direction alongwhich it would normally deflect. This displacement can also be detectedby a position sensitive detector. FIG. 5 also illustrates thelengthening of the path through the sample as a result of the surfacedisplacement (uniform or non-uniform).

FIG. 6 illustrates a configuration which is based on FIGS. 1, 2 and 3,and is a preferred implementation of a “normal incidence, dualwavelength” system. The source 10′ (FIG. 1b) is frequency doubled usingthe nonlinear crystal 24, such as BBO, KTP or LBO. The pump and probebeams are separated by the dichroic mirror 26 such that the doubledwavelength is passed to become the probe beam 21 b, and the undoubtedpart is reflected to become the pump beam 21 a. The pump beam 21 a ismodulated by modulator 90 and is directed at normal incidence onto thesample 51 through objective 98. The probe beam polarization is rotatedby means of a half wave plate 38 and is then passed through a polarizer42 oriented to be orthogonal to the pump beam polarization. Thisretarder/polarizer combination is also used as a variable attenuator forthe probe beam 21 b. The probe beam 21 b is then sent to the variabledelay stage 44, and is focused onto the sample 51 through the samenormal incidence objective 98 as the probe beam 21 a. The reflectedprobe beam 21 b′ is directed to the detector 60 by a dichroic mirror 92which passes the reflected pump beam 21 a, thereby effectively filteringout any reflected probe light. A filter 94 which passes only the probebeam wavelength is placed before the detector 60. The detector 60 isfollowed by the tuned filter 62, lockin amplifier 64, and processor 66,as in FIG. 2.

FIG. 7 illustrates an embodiment of this invention wherein the pump beam21 a and the probe beam 21 b are directed to the sample 51 by means oftapered optical fibers 100 and 102, respectively, to achieve near-fieldfocusing and FS sizes of order 100 nm. The probe beam 21 b is shownhaving normal incidence, and may have a different wavelength than thepump beam 21 a. In this embodiment a terminal portion of the pump and/orprobe beam delivery fiber 100, 102 is reduced in diameter, such as bystretching the fiber, so as to provide a focussed spot FS having adiameter that is less than the normal range of optical focussing. Thisenables the pump and/or probe optical pulse to be repeatably deliveredto a very small region of the sample's surface (e.g., to a spot having adiameter > one micrometer), regardless of any changes that are occurringin the optical path length of the pump and/or probe beam.

The pump beam 21 a need not be brought in through a fiber, and in onemode of operation may be much larger than the probe spot size on thesample. The probe beam 21 b may then be scanned by x-axis and y-axispiezoelectric actuators 102 a and 102 b on a very small spatial scale(similar to a Scanning Tunneling Microscope) with the pump beam locationfixed. This embodiment may be used to map structures patterned in two ormore dimensions on a length scale smaller than can be achieved usingconventional lithography. Therefore, it can be used to map the smalleststructures found in integrated circuits.

The probe beam 21 b can be an expanded beam that is focused onto thefiber 102 by a lens 104, and the reflected probe beam 21 b′ is directedthrough the fiber 102 and is diverted by a splitter 106 to a filter 108and then to the detector 60.

FIG. 12 shows an interface 82 between a patterned structure 84 on top ofthe substrate 80, and is useful in explaining the use of this inventionwhen characterizing three dimensional structures as opposed to planarstructures. The patterned structure may be evaluated by generating astress wave in the substrate 80 and detecting the stress wave in thestructure 84; or by generating the stress wave in the structure 84 anddetecting the stress wave in the structure 84; or by generating thestress wave in the structure 84 and detecting the stress wave in thesubstrate 80.

FIG. 13 shows an interface 82 surrounding a structure 84 formed within apatterned recess within a surface of substrate 80. An example of thisthree dimensional configuration is a tungsten via formed in a hole in aglass layer by (i) depositing the glass on a substrate, (ii) patterningand etching the hole, (iii) depositing a film of tungsten and (iv)polishing the tungsten layer until the glass is exposed (adhesionpromoting layers may be deposited before the tungsten) The structure maybe evaluated by generating the stress wave in the substrate 80 (notapplicable if the substrate, as in the above tungsten example, is glass)and detecting it in the embedded structure 84; or by generating thestress wave in the structure 84 and detecting the stress wave in thestructure 84; or by generating the stress wave in the structure 84 anddetecting the stress wave in the substrate 80.

It should be realized that, in the three dimensional structuresillustrated in FIGS. 12 and 13, the pump beam can also be employed toexcite the normal modes in the structure, which can in turn affect thetransmitted or reflected probe beam.

When applying the probe beam 21 b to the structure 84 it may beadvantageous to use a near-field focussing arrangement, such as thetapered optical fiber shown in FIG. 7. In this case the pump beam FS canbe significantly larger than the probe beam FS, thereby enabling theselective probing of small scale structures.

This capability for spatial imaging can be exploited to performmeasurements of static stress with lateral spatial resolution to 100 nmscale and below.

It is also within the scope of this invention to apply a pump beam FSand a probe beam FS to simultaneously probe a plurality of patternedstructures (e.g., a two-dimensional array of tungsten vias 0.5 μm indiameter and 1.0 μm apart that are formed in a substrate). In this caseeach tungsten via may be considered a separate, independent oscillator,each of which contributes to the reflected or transmitted probe beamsignal. For closer spacings between elements, a “superlattice”-type ofvibrational mode can be excited, wherein the reflected or transmittedprobe signal includes coupling effects between the vias. In either casethe probe beam signal can be compared to a signal obtained from areference “known good” structure, or to a simulation of the structure,or from a combination of reference data and simulations. Any deviationin the probe signal from the reference and/or simulated signal mayindicate that the sample differs in some way from what was expected.

FIG. 14 shows that for samples considered in the ultrasonic technique, amultilayer thin film 84 a, 84 b may be substituted for a simple film 84.Such multilayer films may be formed intentionally by sequentialdepositions, or unintentionally because the substrate 80 may have beenineffectively cleaned prior to succeeding layer depositions, or by the(intentional or unintentional) chemical reaction between two or morelayers (for example, following heat treatment). Such layers may giverise to ultrasonic echoes having complicated shapes and temporalcharacteristics. It is possible to determine the thicknesses andinterface characteristics for thin film structures containing, byexample, five or more sublayers. This is preferably accomplished bycomparing the reflectivity or transmission data with simulations of theultrasonics and detection physics to obtain a best fit set of unknownswith the obtained data.

In the system configurations which use the AOM 40 to modulate the pumpbeam 21 a, there may be no relationship between the modulation rate andthe repetition rate of the laser 12. As a result, the laser pulse trainand modulation cycle are asynchronous. It is possible to make this asynchronous system by deriving the modulation rate from the pulserepetition rate. The pulse repetition rate may be obtained from thelaser 12 by means of an optical detector which senses the emittedpulses, or by using the drive signal from an actively mode-locked laser.To derive the modulation signal, the pulse rate signal is applied to acounter which changes the state of the modulator 40 after n laser pulsesare counted. The modulation rate is then 1/2n times the laser pulserate. In such a synchronous scheme the number of pump pulses impingingon the sample 51 in any period of the modulator 40 is always the same.This eliminates a potential source of noise in the modulated probe beam21 b which might arise in an asynchronous system under conditions inwhich the laser energy contained within a single cycle of the modulator40 varies from period to period of the modulation.

A major source of noise is scattered pump light which can reach theprobe beam detector (a) despite having a nominally orthogonalpolarization (polarizers are not perfect, and also the sample 51 maytend to depolarize the light). As was described above, one technique tosuppress this source of noise is to use pump and probe beams ofdifferent color, so that the pump color may be blocked by means of afilter before the probe detector.

Another method is to modulate the probe beam 21 b at a frequencydifferent from the pump beam modulation frequency. By example, if thepump modulation frequency is f₁ and the probe modulation frequency isf₂, then the part of the probe beam modulated by the pump beam at thesample 51 will have a component at the frequency f₁−f₂. This signal maybe passed through a synchronous demodulator or low pass filter designedto reject f₁ and f₂ and pass only their difference frequency. Thus, anypump light scattered by the sample 51 onto the probe detector (a), whichwould otherwise appear as noise in the data, is suppressed. To minimizethe introduction of ubiquitous 1/f noise the difference frequency ispreferably not below a few hundred kHz. Exemplary frequencies are f₁=1MHz and f₂=500 kHz.

For a sample 51 with the property that the incident light penetrates atleast one wavelength into a layer or layers into which a stress wave islaunched, it is possible to use picosecond ultrasonics to independentlymeasure the sound velocity and refractive index of said layer or layerswith great precision. The sound velocity may also be used to determinethe elastic modulus. Optical interference between probe light reflectedfrom the surface of the sample and probe light reflected from thetraveling stress wave gives rise to oscillations in the intensity of thereflected probe beam 21 b′ as a function of delay. The period of theseoscillations may be measured very precisely. For a material having anindex of refraction n and sound velocity v_(s) the period of theoscillations is given by: $\begin{matrix}{\tau = \frac{\lambda_{0}}{2{nv}_{s}\cos \quad \theta}} & (2)\end{matrix}$

where λ₀ is the optical wavelength in free space and θ is the anglebetween the direction normal to the surface of the sample 51 and thedirection of light propagation in the sample. Typically one knows θ andλ₀ in advance. Thus, from the observed oscillation period, one candeduce the product nv_(s) with high precision. The value of v_(n)independent of n can be found by measuring τ at a second angle (whichyields a value for n), or by using a published value for n. In addition,from the sound velocity, the elastic modulus c₁₁=ρv_(s) ² of the filmmay be determined (using a previously determined value of p).

In accordance with an aspect of this invention measurements at twoangles are simultaneously made by detecting parts of the probe beam 21 bimpinging on the sample 51 within a single focused beam, which thenreflects to two or more closely spaced detectors. It is also within thescope of the invention to controllably tilt the sample stage 50, and tothus cause the probe beam 21 b to impinge on the surface of the sample51 at two or more different angles of incidence.

An alternative technique for determining n and v_(s) has been describedby Grahn et al. (APL 53, no. 21 (Nov. 21, 1988), pp. 2023-2024, and APL.53, no. 23, (Dec. 5, 1988), pp. 2281-2283). However, the Grahn et al.technique depends on the use of an independently-determined thicknessfor the film.

Representative samples for which these techniques may be used areillustrated in FIGS. 15a-15 d.

In FIG. 15a a stress pulse is launched from the film layer 84 by theabsorption of the pump beam energy, and propagates within the substrate80 with a characteristic velocity v_(s). The application of the probebeam pulse 21 b results in two reflections, one from the surface of thefilm 84 and another from the stress pulse. As the stress pulse continuesto propagate away from the film layer 84, the part of the probe pulsereflected at the stress wave has a changing phase shift relative to theprobe pulse reflecting from the film's surface. One result is thatconstructive and destructive interference occurs between the probe pulsereflected from the surface and that reflected from stress wave, therebygiving a variation in the intensity of the probe pulse measured by thedetectors as the stress pulse propagates.

In FIG. 15b the pump pulse launches the stress pulse either by beingapplied to the film surface or to the lower surface of the non-absorbingsubstrate 80. For the latter case the pump pulse propagates through thesubstrate 80 and is absorbed in the film 84, thereby generating thestress pulse. In either case the probe pulse is applied to the lowersurface of the substrate 80, and gives rise to three temporallyseparated reflected probe beams 21 b′.

In FIG. 15c the substrate 80 is assumed to at least weakly absorb thepump pulse, giving rise to the stress pulse in the substrate. Byexample, the substrate 80 may be comprised of silicon.

In FIG. 15d a buried film 84 absorbs the pump pulse and launches astress pulse that propagates towards the surface of an overlyingtransparent film 84′. The resulting reflected probe pulses 21 b′ aresimilar to the case shown in FIG. 21b.

It should be noted that the teachings of this invention apply as well tovery thin films that essentially vibrate when excited rather thansupporting propagating stress or sound pulses.

In accordance with an interface characterization technique of thisinvention, amplitude information (i.e., the amplitude of the change inthe reflected or transmitted probe beam intensity) is used to drawquantitative conclusions about the condition of buried interfaces orsurfaces. The technique has superior sensitivity, compared toconventional ultrasonic techniques, to very subtle interfacial defects(contaminants, interlayers, roughness, bonding, etc.) because thewavelengths of the acoustic phonon comprising the pulse are much shorterthan wavelengths which can be achieved by other methods. For example, incases where distinct acoustic echoes are seen (e.g., for films thickerthan few optical absorption lengths, and thin enough for an acousticwave to return to the surface before the delay stage 44 runs out ofdelay travel), the echo amplitudes and widths can supply informationabout the smoothness of a buried interface from which it has reflected(see, for example, FIG. 15d).

An important mechanism determining such distortion of echo shapes isdephasing at different parts of the stress front reaching a roughenedinterface (and reflecting toward the surface) at different times. Byincorporating such mechanisms into a simulation of a particularstructure, it is possible to quantify the degree of interface roughness.

As employed herein the roughness of a surface or interlayer may be takento be the RMS height and correlation length parallel to the surface orinterlayer.

It should be noted that the same mechanism can cause echo broadening ifit is the top surface (rather than a buried interface) which is rough.It is thus believed to be possible to distinguish between surfaceroughness-induced echo broadening and interface roughness-induced echobroadening based, for example, on the symmetry of the echoes and acomparison with reference echo shapes and/or simulated echo shapes.

It should be noted that the use of echoes per se is but one exemplarytechnique for characterizing the sample 51. For example, in some samplesdistinct echoes are not seen. However, the characterization of thesample can still be accomplished by comparing the reflected probe signalto reference data and/or simulations.

It is also within the scope of the teaching of this invention to detectroughness, or to detect variations in film thickness over small lateraldisplacements, through the use of a small area optical generator anddetector which are scanned relative to the sample surface.

Interfacial layers are another potential cause of echo distortion. As inthe preceding example, a preferred method to characterize suchinterfacial layers is to include them in a model of the sample structure(e.g. as a distinct film having certain physical properties, some ofwhich may be of interest, and so may be left as fitting parameters).

In this regard it should be noted that Tas et al. reported detectingthin interfacial layers of CF_(X) between aluminum and silicon as aparticular example of this effect for a situation in which the aluminumfilms were very thin (G. Tas et al., Appl. Phys. Lett. 61(15), Oct. 12,1992, pp. 1787-1789). Tas et al. did not observe echoes, but rather theringing of the aluminum films. Moreover the result was for a very narrowclass of structures in which the metal films were deposited on top ofhighly uniform, ultrathin layers of very soft material.

Interfacial layers producing much different effects can also becharacterized with the technique of this invention. An important classof interfacial layers include layers which are formed at interfacesbetween two materials which have chemically reacted to form anintermediate compound. As an example, Ti and Al react to form TiAl₃; Tiand Si react to form TiSi₂; Co and Si react to form CoSi₂; Pt and Sireact to form PtSi. The thickness of interfacial layers so formed may besubstantial. By example, in some of the above example pairings thematerials may proceed until one or both of the original materials iscompletely consumed by the reaction.

Interfacial voids, cracks, and regions of poor adhesion may be detectedsimilarly. Such defects usually give rise to acoustic reflections, suchas but not limited to echoes, having larger amplitudes than would beseen for a perfect interface. The reason is that stress pulses exhibitno loss of amplitude when reflected from a perfectly free surface. Assuch, the presence of larger than expected probe signal amplitudeswithin the data can be indicative of, by example, a delamination betweenthe film 84 and an underlying film or substrate.

This technique is also sensitive to thin film processes that areintended to enhance adhesion between layers. One such technique is ionbombardment. It has been found by the inventors that the rate of dampingof ultrasonic ringing of a film deposited on a substrate, and thenimplanted with high energy ions, is more slowly damped for low ion dosesthan for high ion doses. It is inferred that the adhesion is greater forsamples with higher implant doses because the acoustic energy in thethin film is able to couple to the substrate more readily than insamples having lower implant doses or energies.

In summary, an ultrashort laser pulse (τ_(p)˜0.1 psec) is selectivelyabsorbed in a thin film or in a more complex nanostructure. Theabsorption sets up a thermal stress which generates an ultrashort stresswave impulse. The propagating stress can affect the optical constantsanywhere within the sample, causing a complex, but calculable, change inthe reflectivity (or transmission, or polarization state, or opticalphase) of the probe beam. Echoes are but one simple case of temporalfeatures. Other, more complex temporal features may also be detected,such as those that correspond to ultrasonic vibrations in nanostructuresand multilayer samples. These other temporal features may not correspondto a stress pulse returning to the surface. The only requirement fordetection is that the stress generated by the pump is at a depth in thesample where it can interact with the probe beam.

A film or a multilayer deposited on a substrate at an elevatedtemperature is normally in a state of stress due to differential thermalexpansion. Present techniques for evaluating the stress have severepractical limitations.

Measurements on several materials have shown how the temperaturedependence ∂v_(s)/∂T of the sound velocity is affected by stress. Thisquantity can be readily measured by the picosecond ultrasonic methods ofthis invention and can be used to give the stress of the film, withoutthe requirement of knowing the film's precise thickness. The techniquehas many advantages and is applicable even for very thin films,multilayers (˜100 Å), and for submicron lateral dimensions.

Further in accordance with this invention, the sound velocity in a filmis measured at two temperatures in the film. The difference between thetwo sound velocities depends in a predictable way on the stress withinthe film, whether the stress is externally imposed or “built-in”. Thisprovides a method for stress measurement on a lateral scale of the spotsize FS, which may have a diameter of one micron or less. Thetemperature of the sample 51 can be changed via a resistively heatedstage, an arc lamp, a CW laser focused onto the measurement spot, or bymodulating the pump power. The sound velocity can be measured byobserving ultrasonic echoes, or oscillatory signals as disclosed inregard to FIGS. 15a-15 d, or the vibrational period of very thin films.

The rate of change of the sound velocity with temperature depends on thestress in the film in a predictable way, as has been reported in theliterature (Salama K. et al., Journal of Applied Physics vol. 51, page1505 et seq. (1980); J. Cantrell, Ultrasonics International 1989Conference Proceedings, pp. 977 et seq.).

Picosecond ultrasonics measurements of the sound velocity may be made inthe following ways: echo time (as in Tauc et al.); ringing period; theoscillation period of oscillations caused by a travelling stress wave insemitransparent or transparent samples, or by producing a best fit topicosecond ultrasonic data by varying a sound velocity parameter in asimulation of one or more layers.

The temperature may be changed in the following ways: by a resistiveheater embedded in the sample stage 50; by an inductive heater;radiatively (i.e. an intense lamp) ; by varying the pump beam intensitysuch that the mean temperature of the sample is above the ambient; or byintroducing a continuous wave heating laser onto the measurement spot FSthrough a common or separate objective.

The temperature change may be measured in the following ways: by opticalpyrometry; by a calculation of the deposited heating energy (whichrequires measurement of the incident and reflect radiation) and thenusing the values of the optical and thermal constants of the sampleneeded to determine the equilibrium temperature in the measurementregion; with a thermocouple (in contact with the sample 51); or usingthe Mirage Effect. In the Mirage Effect the change in the refractiveindex in the air above the heated spot is measured via the deflection ofa laser beam incident at a glancing angle, and the temperature isdeduced from the refractive index change necessary to produce anobserved beam deflection (see, for example, T. R. Anthony et al.,Physical Review B, vol. 42, 1104 (1990)).

Calibration of the system of this invention can be accomplished inseveral manners. By example, films comprised of several different metalscan be deposited on silicon wafers at different temperatures. In thesesamples, the stress can be independently estimated by calculation fromdifferential expansion and from measurements of film-induced curvature.The calculated values are then compared with results obtained from theuse of the system of this accordingly.

The teaching of this invention also includes methods and apparatus formeasuring the change in the optical constants of a material with strain.In this technique the system is used to determine the quantities ∂n/∂ηand ∂κ/∂η in a particular sample geometry. Samples have a film of glass,or another transparent material deposited on top of a thin film ofopaque or semi-opaque material (the material of interest may be ametal). The optical constants of both materials are known. Thequantities ∂n/∂η and ∂κ/∂η are also known for the transparent material,and are deduced for the second material by comparing acoustic data withsimulations in which ∂n/∂η and ∂κ/∂η for the second material are varied.

To be able to carry out simulations which enable a quantitativecomparison with data of the magnitude of the change in the reflectivityor transmissivity of a sample in which a stress pulse is generated, itis necessary to know in advance by how much the optical constant n and κfor the subject materials change in response to stress σ. It ispreferable in some embodiments to carry out simulations in terms of thestrain η, which may be related to the stress in a simple way. In termsof the strain, the foregoing is equivalent to the statement that thequantities ∂n/∂η and ∂κ/∂η must be known. It is a feature of thisinvention that the methods and apparatus described herein may be used todetermine these quantities. In one technique, an/an and ∂κ/∂η may befound for a material by depositing on top of an optically smoothspecimen of this material a layer of transparent material such as aglass (e.g. LP-CVD TEOS, or PE-CVD BPSG) having a thickness of at leastseveral hundred Angstroms, and less than 100 microns. The underlyingspecimen of material for which ∂n/∂η and ∂κ/∂η are to be determined maybe a thin film, or a thick substrate. The process of determining ηn/∂ηand ∂κ/∂η involves two steps which may be described in relation to FIG.15d (which shows the case in which the material of interest is a thinmetal film disposed on top of a substrate which may be silicon. In step(1) a stress pulse is generated in the material. Part of this stresswave enters the transparent layer and propagates to the free surface,then reflects from this surface, then propagates through the transparentlayer, and then part of this stress reenters the metal film. The stresspulse reflecting from the free surface has the opposite sign to theincident stress pulse, but identical amplitude. The fraction of thestress pulse incident from the glass layer on the metal film whichreenters the metal film may be calculated from the acoustic impedances(i.e. the product of the sound velocity and density) of the glass andmetal (as described in Tauc et al.). While the stress wave propagatesthrough the glass layer it gives rise to oscillations as describedpreviously with regard to FIGS. 15a-15 d. The amplitude of theseoscillations may be used to compute the quantity ∂n/∂η for the glass(which in general will have a different value than the valuecorresponding to the metal) either analytically or by comparison withsimulations of the oscillations: ∂κ/∂η=0 for the glass. In step (2) thequantities an/an and ∂κ/∂ηfor the metal layer are determined by carryingout a simulation of the reflectivity change which occurs in response tothe stress reentering this layer, and by adjusting ∂n/∂η and ∂κ/∂η inorder to achieve a best fit to the observed response for times duringwhich the effects of the stress wave on the reflected probe intensitymay be observed. In these simulations the acoustic impedances and soundvelocities of the glass and metal film are assumed to be known inadvance. In addition, the optical constants n and κ for one or bothmaterials at the pump and probe beam wavelengths may be used as inputsto the simulations, or alternatively may be used as further adjustableparameters.

An important feature of this procedure is that simulation parameters sodetermined should simultaneously fit the response corresponding to thestress wave propagating in the metal. In the above procedure it isassumed that the detector 60 and processor 66 are so calibrated as togive the true reflectivity of the sample as a function of time. Analternative three step procedure which does not require the detector 60and processor 66 to be so calibrated is as follows. In step (1) a stresspulse is generated in the material. Part of this stress wave enters thetransparent layer and propagates to the free surface, then reflects fromthis surface, then propagates through the transparent layer, and thenpart of this stress reenters the metal film. The stress pulse reflectingfrom the free surface has the opposite sign to the incident stresspulse, but identical amplitude. The fraction of the stress pulseincident from the glass layer on the metal film which reenters the metalfilm may be calculated from the acoustic impedances (i.e. the product ofthe sound velocity and density) of the glass and metal (as described inTauc et al). While it propagates through the glass layer the stress wavegives rise to oscillations as described previously with regard to FIGS.15a-15 d. In step (2) ∂n/∂η for the glass and ∂n/∂η and ∂κ/∂η for themetal are allowed to be freely varied in the simulated response in orderto achieve a best fit to the observed response. The values ∂n/∂η and∂κ/∂η so obtained may be scaled by the ratio of the true value of ∂κ/∂ηfor the glass to the fitted value. Therefore, in Step (3) the true valueof an/an for the glass is determined (this may be obtained by a numberof methods, other than picosecond ultrasonics, that are applicable totransparent materials), and the fitted ∂n/∂η and ∂κ/∂η for the metal arescaled to obtain their true values.

It is also within the scope of the teaching of this invention to use thederivative of the signal versus time to determine the properties of asample, rather than the signal itself. The purpose is to remove some ofthe background signal, associated with the cooling of the film, from thedata. The derivative of the signal can also be compared with thederivative of a simulation to extract parameters.

In one embodiment of the algorithm used to determine unknown quantitiesfrom the observed reflectivity or transmission of the sample, thetemporal features associated with the propagation of stress within thesample are compared with a simulation which includes only the ultrasonicresponse. Other features, in particular the slowly varying backgroundassociated with diffusion of heat within the sample, are ignored in suchcomparisons, or may be included in the fitting process by introducingone or several fitting parameters of a slowly varying function (e.g. anexponential, or a low order polynomial). For some materials the slowlyvarying background may have a much greater amplitude than the featuresassociated with ultrasonic response of the sample. In order to improvethe accuracy and speed of the fitting process in such situations, it maybe convenient to numerically compute the derivative of the response withrespect to delay time. A comparison may then be made between thederivative so determined and the derivative of the simulated response,and the values of the unknowns varied until a best fit is obtained.

An alternative method is to measure the derivative of the sampleresponse directly, avoiding the step of numerical differentiation. Thismethod provides superior signal to noise in comparison to the numericalprocedure. In one embodiment of this derivative measurement scheme theretroreflector 46 in the probe path is placed on a mount (such as apiezoelectric actuator) which is caused to oscillate rapidly (f₂) (i.e.from 10 to 10⁶ Hz) along the probe beam axis, thus executing a largenumber of oscillations (i.e., greater than 10) for each successive delayposition of the delay mechanism. The signal measured in such a systemmay be related to the derivative of the signal versus delay by a simpleproportionality constant, provided that the amplitude of theoscillations corresponds to a range of delays which are small comparedto the minimum temporal extent of observed ultrasonic features in anundifferentiated response. In this embodiment it is also possible todetect at the difference frequency (f_(1−f) ₂ or f₁+f₂), where f₁ is thefrequency induced by the AOM in the pump beam path (e.g., 1 MHz), and f₂is the frequency induced by the delay modulator in the probe beam path.

Reference is now made to FIG. 16 for illustrating an embodiment of thisinvention which is referred to as a parallel, oblique embodiment.

This embodiment includes an optical/heat source 120, which functions asa variable high density illuminator, and which provides illumination fora video camera 124 and a sample heat source for temperature-dependentmeasurements under computer control. An alternative heating methodemploys a resistive heater embedded in the stage sample stage 122. Theadvantage of the optical heater is that it makes possible rapidsequential measurements at two different temperatures, as will bedescribed below. The video camera 124 provides a displayed image for anoperator, and facilitates the set-up of the measurement system.Appropriate pattern recognition software can also be used for thispurpose, thereby minimizing or eliminating operator involvement.

The sample stage 122 is preferably a multiple-degree of freedom stagethat is adjustable in height (z-axis), position (x and y-axes), and tilt(Θ), and allows motor controlled positioning of a portion of the samplerelative to the pump and probe beams. The z-axis is used to translatethe sample vertically into the focus region of the pump and probe, the xand y-axes translate the sample parallel to the focal plane, and thetilt axes adjust the orientation of the stage 122 to establish a desiredangle of incidence for the probe beam. This is achieved via detectorsPDS1 and PDS2 and the local processor, as described below.

In an alternative embodiment, the optical head may be moved relative toa stationary, tiltable stage 122′ (not shown). This is particularlyimportant for scanning large objects (such as 300 mm diameter wafers, ormechanical structures, etc.) In this embodiment the pump beam, probebeam, and video are delivered to the translatable head via opticalfibers or fiber bundles.

BS5 is a broad band beam splitter that directs video and a small amountof laser light to the video camera 124. The camera 124 and localprocessor can be used to automatically position the pump and probe beamson a measurement site.

The pump-probe beam splitter 126 splits an incident laser beam pulse(preferably of picosecond or shorter duration) into pump and probebeams, and include s a rotatable half-wave plate (WP1) that rotates thepolarization of the unsplit beam. WP1 is used in combination withpolarizing beam splitter PBS1 to effect a continuously variable splitbetween pump and probe power. This split may be controlled by thecomputer by means of a motor to achieve an optimal signal to noise ratiofor a particular sample. The appropriate split depend on factors such asthe reflectivity and roughness of the sample. Adjustment is effected byhaving a motorized mount rotate WP1 under computer control.

A first acousto-optic modulator (AOM1) chops the pump beam at afrequency of about 1 MHz. A second acousto-optic modulator (AOM2) chopsthe probe beam at a frequency that differs by a small amount from thatof the pump modulator AOM1. The use of AOM2 is optional in the systemillustrated in FIG. 16. As will be discussed below, the AOMs may besynchronized to a common clock source, and may further be synchronizedto the pulse repetition rate (PRR) of the laser that generates the pumpand probe beams.

A spatial filter 128 is used to preserve at its output a substantiallyinvariant probe beam profile, diameter, and propagation direction for aninput probe beam which may vary due to the action of the mechanicaldelay line shown as the retroreflector 129. The spatial filter 128includes a pair of apertures A1 and AOM2, and a pair of lenses L4 andL5. An alternative embodiment of the spatial filter incorporates anoptical fiber, as described above. WP2 is a second adjustable half waveplate which functions in a similar manner, with PBS2, to the WP1/PBS1 ofthe beamsplitter 126. With WP2 the intent is to vary the ratio of thepart of the probe beam impinging on the sample to that of the portion ofthe beam used as a reference (input to D5 of the detector 130. WP2 maybe motor controlled in order to achieve a ratio of approximately unity.The electrical signals produced by the beams are subtracted, leavingonly the modulated part of the probe to be amplified and processed. PSD2is used in conjunction with WP2 to achieve any desired ratio of theintensities of the probe beam and reference beam. The processor mayadjust this ratio by making a rotation of WP2 prior to a measurement inorder to achieve a nulling of the unmodulated part of the probe andreference beam. This allows the difference signal (the modulated part ofthe probe) alone to be amplified and passed to the electronics.

The beamsplitter BS2 is used to sample the intensity of the incidentprobe beam in combination with detector D2. The linear polarizer 132 isemployed to block scattered pump light polarization, and to pass theprobe beam. Lenses L2 and L3 are pump and probe beam focusing andcollimating objectives respectively. The beamsplitter BS1 is used todirect a small part of pump and probe beams onto a first PositionSensitive Detector (PSD1) that is used for autofocusing, in conjunctionwith the processor and movements of the sample stage 122. The PSD1 isemployed in combination with the processor and the computer-controlledstage 122 (tilt and z-axis) to automatically focus the pump and probebeams onto the sample to achieve a desired focusing condition.

The detector D1 may be used in common with acoustics, ellipsometry andreflectometry embodiments of this invention. However, the resultantsignal processing is different for each application. For acoustics, theDC component of the signal is suppressed such as by subtractingreference beam input D5, or part of it as needed, to cancel theunmodulated part of D1, or by electrically filtering the output of D1 soas to suppress frequencies other than that of the modulation. The smallmodulated part of the signal is then amplified and stored. Forellipsometry, there is no small modulated part, rather the entire signalis sampled many times during each rotation of the rotation compensator(see FIG. 17), and the resulting waveform is analyzed to yield theellipsometric parameters. For reflectometry, the change in the intensityof the entire unmodulated probe beam due to the sample is determined byusing the D1 and D2 output signals (D2 measures a signal proportional tothe intensity of the incident probe). Similarly, additionalreflectometry data can be obtained from the pump beam using detectors D3and D4. The analysis of the reflectometry data from either or both beamsmay be used to characterize the sample. The use of two beams is usefulfor improving resolution, and for resolving any ambiguities in thesolution of the relevant equations.

A third beamsplitter BS3 is used to direct a small fraction of the pumpbeam onto detector D4, which measures a signal proportional to theincident pump intensity. A fourth beamsplitter BS4 is positioned so asto direct a small fraction of the pump beam onto detector D3, whichmeasures a signal proportional to the reflected pump intensity.

FIG. 17 illustrates a normal pump beam, oblique probe beam embodiment ofthis invention. Components labelled as in FIG. 16 function in a similarmanner, unless indicated differently below. In FIG. 17 there is providedthe above-mentioned rotation compensator 132, embodied as a linearquarter wave plate on a motorized rotational mount, and which forms aportion of an ellipsometer mode of the system. The plate is rotated inthe probe beam at a rate of, by example, a few tens of Hz tocontinuously vary the optical phase of the probe beam incident on thesample. The reflected light passes through an analyzer 134 and theintensity is measured and transferred to the processor many times duringeach rotation. The signals are analyzed according to known types ofellipsometry methods to determine the characteristics of the sample(transparent or semitransparent films). This allows the (pulsed) probebeam to be used to carry out ellipsometry measurements.

In accordance with an aspect of this invention the ellipsometrymeasurements are carried out using a pulsed laser, which isdisadvantageous under normal conditions, since the bandwidth of thepulsed laser is much greater than that of a CW laser of a type normallyemployed for ellipsometry measurements.

When acoustics measurements are being made, the rotation compensator 132is oriented such that the probe beam is linearly polarized orthogonal tothe pump beam.

The analyzer 134 may be embodied as a fixed polarizer, and also forms aportion of the ellipsometer mode of the system. When the system is usedfor acoustics measurements the polarizer 134 is oriented to block thepump polarization. When used in the ellipsometer mode, the polarizer 134is oriented so as to block light polarized at 45 degrees relative to theplane of the incident and reflected probe beam.

Finally, the embodiment of FIG. 17 further includes a dichroic mirror(DM2), which is highly reflective for light in a narrow band near thepump wavelength, and is substantially transparent for other wavelengths.

It should be noted in FIG. 17 that BS4 is moved to sample the pump beamin conjunction with BS3, and to reflect a portion of the pump to D3 andto a second PSD (PSD2). PSD2 (pump PSD) is employed in combination withthe processor, computer controlled stage 122 (tilt and z-axis), and PSD1(Probe PSD) to automatically focus the pump and probe beams onto thesample to achieve a desired focusing condition. Also, a lens L1 isemployed as a pump, video, and optical heating focussing objective,while an optional lens L6 is used to focus the sampled light from BS5onto the video camera 124.

Reference is now made to FIG. 18 for illustrating a further embodimentof the picosecond ultrasonics system, specifically a single wavelength,normal pump, oblique probe, combined ellipsometer embodiment. As before,only those elements not described previously will be described below.

Shutter 1 and shutter 2 are computer controlled shutters, and allow thesystem to use a He—Ne laser 136 in the ellipsometer mode, instead of thepulsed probe beam. For acoustics measurements shutter 1 is open andshutter 2 is closed. For ellipsometer measurements shutter 1 is closedand shutter 2 is opened. The HeNe laser 136 is a low power CW laser, andhas been found to yield superior ellipsometer performance for somefilms.

FIG. 19 is a dual wavelength embodiment of the system illustrated inFIG. 18. In this embodiment the beamsplitter 126 is replaced by aharmonic splitter, an optical harmonic generator that generates one ormore optical harmonics of the incident unsplit incident laser beam. Thisis accomplished by means of lenses L7, L8 and a nonlinear opticalmaterial (DX) that is suitable for generating the second harmonic fromthe incident laser beam. The pump beam is shown transmitted by thedichroic mirror (DM 138 a) to the AOM1, while the probe beam isreflected to the retroreflector. The reverse situation is also possible.The shorter wavelength may be transmitted, and the longer wavelength maybe reflected, or vice versa. In the simplest case the pump beam is thesecond harmonic of the probe beam (i.e., the pump beam has one half thewavelength of the probe beam).

It should be noted that in this embodiment the AOM2 is eliminated sincerejection of the pump beam is effected by means of color filter F1,which is simpler and more cost effective than heterodyning. F1 is afilter having high transmission for the probe beam and the He—Newavelengths, but very low transmission for the pump wavelength.

Finally, FIG. 20 illustrates a normal incidence, dual wavelength,combined ellipsometer embodiment of this invention. In FIG. 20 the probebeam impinges on PBS2 and is polarized along the direction which ispassed by the PBS2. After the probe beam passes through WP3, a quarterwave plate, and reflects from the sample, it returns to PBS2 polarizedalong the direction which is highly reflected, and is then directed to adetector D0 in detector block 130. D0 measures the reflected probe beamintensity.

In greater detail, WP3 causes the incoming plane polarized probe beam tobecome circularly polarized. The handedness of the polarization isreversed on reflection from the sample, and on emerging from WP3 afterreflection, the probe beam is linearly polarized orthogonal to itsoriginal polarization. BS4 reflects a small fraction of the reflectedprobe onto an Autofocus Detector AFD.

DM3, a dichroic mirror, combines the probe beam onto a common axis withthe illuminator and the pump beam. DM3 is highly reflective for theprobe wavelength, and is substantially transparent at most otherwavelengths.

D1, a reflected He—Ne laser 136 detector, is used only for ellipsometricmeasurements.

It should be noted that, when contrasting FIG. 20 to FIGS. 18 and 19,that the shutter 1 is relocated so as to intercept the incident laserbeam prior to the harmonic splitter 138.

Based on the foregoing descriptions of a number of embodiments of thisinvention, it can be appreciated that this invention teaches, in oneaspect, a picosecond ultrasonic system for the characterization ofsamples in which a short optical pulse (the pump beam) is directed to anarea of the surface of the sample, and then a second light pulse (theprobe beam) is directed to the same or an adjacent area at a later time.The retroreflector 129 shown in all of the illustrated embodiments 16-20can be employed to provide a desired temporal separation of the pump andprobe beams, as was described previously with regard to, by example,FIG. 9.

The system measures some or all of the following quantities: (1) thesmall modulated change ΔR in the intensity of the reflected probe beam,(2) the change ΔT in the intensity of the transmitted probe beam, (3)the change ΔP in the polarization of the reflected probe beam, (4) thechange ΔΦ in the optical phase of the reflected probe beam, and/or (5)the change in the angle of reflection Δβ of the probe beam. Thesequantities (1)-(5) may all be considered as transient responses of thesample which are induced by the pump pulse. These measurements can bemade together with one or several of the following: (a) measurements ofany or all of the quantities (1)-(5) just listed as a function of theincident angle of the pump or probe light, (b) measurements of any ofthe quantities (1)-(5) as a function of more than one wavelength for thepump and/or probe light, (c) measurements of the optical reflectivitythrough measurements of the incident and reflected average intensity ofthe pump and/or probe beams; (d) measurements of the average phasechange of the pump and/or probe beams upon reflection; and/or (e)measurements of the average polarization and optical phase of theincident and reflected pump and/or probe beams. The quantities (c), (d)and (e) may be considered to be average or static responses of thesample to the pump beam.

One function of the system is to determine the thickness of the filmsmaking up the sample, the mechanical properties of the films (soundvelocities and densities), and the characteristics of the interfaces(adhesion, roughness, and other interfacial characteristics).

The system in accordance with the various embodiments of this inventionthus enables a combination of measurements of the type listed above soas to enable the determination of properties of the sample that are notobtainable through the use of conventional systems.

By example, consider a sample in which the upper-most film istransparent. In such a sample the pump pulse will not be absorbed inthis film, but will instead be absorbed in the next underlying film,assuming that this film is not also transparent. There will, however,normally be a contribution to the change ΔR in reflectivity of the probepulse from the uppermost transparent film. A stress wave will begenerated in the underlying optically-absorbing film and will propagateinto the transparent film. This will cause a local change Δn in therefractive index n of the transparent film, and the location of thischange in the refractive index will propagate towards the free surfaceof the transparent film with a speed equal to the sound velocity v inthe film. Probe light which is reflected at this change in n willinterfere constructively or destructively with the probe light which isreflected at the other interfaces of the sample. As a consequence therewill be a change ΔR in the intensity of the reflected probe light, whichchange will amount to an oscillation of frequency f given by$f = {2{nv}\quad \cos \frac{\alpha}{\lambda}}$

where λ is the wavelength in free space of the probe light and θ is theangle between the direction of the probe light in the sample and thenormal to the surface. Hence a measurement of the frequency of thisoscillation can be used to determine the product nv, but not n and vseparately. This oscillation will suffer an abrupt change in phase whenthe stress pulse reaches the free surface of the sample at time τ₁ andis then reflected back. By a measurement of τ₁ one can thus determinethe quantity d/v, where d is the film thickness. These two measurementsand their analysis may be obtained using conventional systems, but donot lead to definite values for the three quantities of interest n, v,and d. The present invention overcomes this difficulty as follows.

If measurements are made of the frequency f as a function of the angleof incidence θ of the probe light outside the sample the measured f(θ)can be analyzed to give both n and v. This is because the relationbetween α and θ involves only n and not v. Then the measurement of thetime τ₁ can be used to determine d.

Second, using measurements of the intensity of the reflected pump orprobe light, the phase change or the relative intensities of thedifferent polarization components of the pump and/or probe light canalso be used in many circumstances to deduce the refractive index and/orthe thickness of the transparent film. For example, the thickness oroptical constants of one or more layers in a sample may be determinedfrom the measured quantities according to the principles of opticalreflectometry or ellipsometry. In this case the picosecond light pulsesavailable in the system of this invention can be used to make suchreflectometry or ellipsometry measurements, and extra light sources maynot be needed. The pulsed nature of the lasers is not relevant to thesemeasurements. The determination of the optical constants and/or filmthicknesses then enables the sound velocity and/or the thickness to bededuced from a single measurement of the frequency f.

The foregoing example has been described in terms of a measurement ofΔR(t); clearly the same technique may be applied to the other transientquantities.

For many samples of current interest in the semiconductor circuitfabrication industry it is not practical to measure the change ΔT in thetransmission of the probe light pulse. The films are normally depositedonto silicon substrates of thickness around 0.02 cm. Unless light ofwavelength of one micron or greater is used, the light will be heavilyabsorbed in the substrate making the measurement of the transmissionvery difficult. For such samples conventional methods are thusessentially limited to the use of the measurement of the change ΔR inthe optical reflectivity induced by the pump pulse. Many samples ofinterest include a series of films deposited sequentially onto thesubstrate. This type of structure can be referred to as a “stack”. Whenstress pulses are generated in a stack a very complicated response (forexample, the result of a measurement of ΔR(t)) may be obtained. Thiscomplex response results from the generation of stress pulses in variousdifferent parts of the structure, the propagation of these pulses withpartial transmission and partial reflection across the interfaces intoother films, and the change in the intensity reflection coefficient ofthe structure due to the strain-induced change in the optical propertiesof each film. To determine the thickness of a number of the films in astack requires the determination of the times at which stress pulsesoriginating at known places in the structure are reflected ortransmitted at the various interfaces. From these times, and usingassumed velocities for the different films, the thicknesses of the filmscan be found. The determination of the times just referred to requiresthe identification of the different features that appear in the responseΔR(t). With the arrangement available in conventional systems theidentification of the origin of the various features may be extremelydifficult and/or time-consuming for a multi-layer structure. It is oftennecessary to make a guess that a particular feature arises from a stresspulse which originates at a particular location and has undergone acertain sequence of transmissions and reflections at differentinterfaces. In addition, it may be the case that a certain feature ofinterest, such as the arrival of a stress pulse at one particularinterface, gives a response which happens to be dominated or masked by alarger response from another stress pulse reaching a different part ofthe structure at approximately the same time. The present inventionovercomes these difficulties as follows.

As mentioned above, in the prior art the primary measured quantity formost samples of current technical interest is the change ΔR(t) inoptical reflectivity. If the response ΔR(t) is difficult to analyze,then it is also difficult to deduce the required information about thestructure, for example the thicknesses of the different films. Thisdifficulty may be overcome by measurements of ΔP, ΔΦ, or Δβ. Forexample, a particularly important feature may appear as a very smallresponse in ΔR(t), but may make a dominant response in ΔP(t), ΔΦ(t), orΔβ(t).

In accordance with an aspect of this invention the non-destructivesystem and method is enabled to also simultaneously measure at least twotransient responses of the structure to the pump pulse. Thesimultaneously measured transient responses comprise at least two of ameasurement of the modulated change ΔR in an intensity of a reflectedportion of a probe pulse, the change ΔT in an intensity of a transmittedportion of the probe pulse, the change ΔP in the polarization of thereflected probe pulse, the change ΔΦ in optical phase of the reflectedprobe pulse, and the change in an angle of reflection Δβ of the probepulse. The measured transient responses are then associated with atleast one characteristic of interest of the structure.

However, even when the measurement of ΔP(t), ΔΦ(t), or Δβ(t) does notshow a response in which the feature of primary interest dominates, itmay still be possible to effectively isolate the response of interest bya “differential method” (DM). That is, by taking a suitable linearcombination of the different measured responses it may be possible toenhance the magnitude of the response of interest and reduce the size ofthe other competing response or responses.

The same type of DM procedure as just described can also be accomplishedby making simultaneous or sequential measurements of one or more of thequantities ΔR(t), etc. at more than one wavelength of the pump and/orthe probe, or angle of incidence of the pump and/or the probe, orpolarization of the pump and/or the probe beams.

The same type of DM procedure can also be achieved for some samples bymaking measurements at more than one intensity of the pump and/or probebeams. The point is that the responses, such as the change inreflectivity ΔR(t), for example, may vary non-linearly with theintensity and/or the duration of the pump and/or probe pulses. Thus,again by taking suitable linear combinations of the responses measuredat different intensities or pulse durations, it may be possible toenhance a portion of the response arising from one effect at the expenseof competing effects.

The picosecond ultrasonic system in accordance with the teaching of thisinvention can also employ the simultaneous or sequential measurement ofthe ellipsometric parameters of the sample using signals correspondingto one or more suitable non-pulsed additional light sources (e.g., theHe—Ne laser 136) whose optical path may or may not have some or alloptical components in common with the means for directing the pulsedlaser beams to and from the sample. This overcomes some of thedifficulties of conventional systems in a manner similar to the methodsdescribed above.

An automatic adjustment of the position and orientation of the sample toachieve a desired overlap of the pump and probe beams on the samplesurface can also be employed, in conjunction with the control of thespot size on the sample of one or both of the pump and probe lasers.This is accomplished, as described in reference to FIGS. 16-20, with ameans for detecting one or both beams after they impinge on the sample,and a means for adjusting the height and tilt of the sample with respectto the beams to achieve the desired focusing conditions. This approachis superior to the manual adjustment techniques taught by the prior art,in that an automatic adjustment scheme overcomes the difficulty of aslow and unreliable manual adjustment which is incompatible with theneed to make rapid and accurate measurements in an industrialenvironment. Furthermore, the reproduceability of measurements betweensamples is also improved.

It is also within the scope of this invention to provide a picosecondultrasonics system using one or more modulators of the pump or probebeams in which the modulation drive signal for one or more of themodulators, and the pulse rate of one or more pulsed lasers, are derivedfrom a common clock. In addition, it is also within the scope of theteaching of this invention that the modulation of the pump or probe beamis derived from the pulse rate of one or more of the pulsed lasers inthe system. This overcomes a problem in the prior art, wherein themodulation is not synchronized with the repetition rate of the laser orlasers. Thus, in each modulation cycle there can be a variation in thenumber of probe or pump pulses contained in one modulation cycleaccording to the instantaneous phase of the modulator relative to thetiming of the laser pulses. This variation contributes to the noise ofthe system, and is advantageously eliminated in the present invention.

This invention further teaches a picosecond ultrasonic system in whichmeasurements for a particular sample are made at at least twotemperatures for the purpose of detecting the change in the soundvelocity in one or more layers in response to the temperature change.The temperature change may be induced by a heat lamp directed at thesurface of the sample, by a resistive heater in contact with the rear ofthe sample, by the average heating of the sample by the pump lightpulses, or by the use of another light source directed through some ofthe same optical elements used to guide the pump and/or probe beams ontothe sample (or via some other optical system). The stress in one or morelayers is determined by relating the observed change in the soundvelocity in one or more layers determined at two or more temperatures tothe stress in the layer or layers.

As has been described, it has been established experimentally that thetemperature-dependence of the sound velocity depends on the staticstress. This provides the basis for this aspect of the invention.

It is important to note that the application of this method does notrequire a measurement of the absolute value of the sound velocity, butonly the change of the velocity with temperature. This is an importantpoint, since to determine the absolute velocity it would be necessary tohave a very precise value for the film thickness. To determine thetemperature-dependence of the sound velocity, on the other hand,requires only a measurement of the temperature-dependence of theacoustic transit time. To determine the temperature-dependence of thesound velocity from this quantity it is necessary only to apply acorrection to allow for the thermal expansion of the sample.

This invention further teaches a picosecond ultrasonic system whichdirectly measures the derivative with respect to time delay between thepump and probe beams of some or all of the quantities listed above,i.e., (1) the small modulated change ΔR in the intensity of thereflected probe beam, (2) the change ΔT in the intensity of thetransmitted probe beam, (3) the change ΔP in the polarization of thereflected probe beam, (4) the change ΔΦ in the optical phase of thereflected probe beam, and/or (5) the change in the angle of reflectionΔβ of the probe beam. To achieve the measurement of the derivative theprobe pulse delay is varied periodically over a small range by means ofan oscillating optical component in the pump or probe path. A frequencyrange of 10 Hz to 1 MHz is suitable for this purpose.

One advantage of this method is as follows. In many applications one isinterested in the time of arrival of acoustic echoes at certain pointsin the sample. These acoustic echoes appear as sharp features in themeasured reflectivity change ΔR(t) as a function of time. These echoescan be enhanced relative to the background if the system directlymeasures the derivative of ΔR (or the other quantities listed above)with respect to time, rather than ΔR itself.

This invention further teaches a picosecond ultrasonic system whichincorporates an optical fiber or fibers for any of the followingpurposes: (a) guiding the laser beam between different parts of theoptical system; (b) guiding the pump and/or probe to the sample; (c)collecting the reflected or transmitted probe from the sample; and/or(d) maintaining a constant probe output profile and position for varyinginput conditions.

The picosecond ultrasonic system in accordance with this invention mayincorporate light sources with any of the following features.

A first feature employs a pulsed laser with the output directed to anoptical harmonic generator or generators, as in FIGS. 19 and 20. Theoutputs of the harmonic generator 138 and/or the unmodified output ofthe laser are thus used for the pump and/or probe beams. This improveson conventional practice in that it allows for the rejection of the pumplight at the detector of the probe beam so as to improve the signal tonoise ratio. Also, for certain samples the most advantageous wavelengthfor the generating pump beam may be different from the optimumwavelength for the probe beam.

A second feature employs one or more of the polarizing beam splitterswhich are used to continuously vary the ratio of the pump and probebeams under computer control. The ratio can be controlled to optimizethe signal to noise for a given sample. It may be advantageous to changethe ratio to achieve the best performance for samples with particularcharacteristics.

This invention further teaches a picosecond ultrasonic system thatincorporates different repetition rate lasers to effect a delay as analternative approach to a mechanical delay stage. This has the advantagethat a mechanical stage is not required. In addition, the data an beacquired very quickly, provided that the signal-to-noise ratio isacceptable.

This invention further teaches a picosecond ultrasonic system thatemploys a multi-element delay stage. This has the advantage that thedelay of the probe pulse is increased for a given di stance moved by themechanical stage. Thus, the distance travelled by the stage in order toproduce a given delay of the probe pulse can be decreased.

Furthermore, the invention teaches the measurement of the transientoptical properties of the sample using a probe pulse that is derivedfrom an output pulse of the laser that is different from the outputpulse used for the pump.

This enables the production of a large effective delay for the probe,without requiring that a very long optical path difference beestablished in the system.

The invention also teaches a picosecond ultrasonic system which mayinclude suitable additional optical sources, including additional lasersas well as white light sources. These sources may be directed to thesample by a guiding system which may include some elements in commonwith the pulsed pump and probe beam paths. These additional lightsources may be used to effect ellipsometry or reflectometry, or toilluminate the sample for inspection purposes, or to raise thetemperature at a particular location.

In one aspect the invention provides a picosecond ultrasonic system thatincorporates the color filter F1 in the path of the probe beam after ithas been reflected or transmitted at the sample for the purpose ofsuppressing scattered pump light. This embodiment is employed toadvantage when the pump and probe sources have different wavelengths.The suppression of the pump light improves the signal to noise ratiowhen the sample surface is non-specular, and where the incident pumplight is scattered at the sample surface.

The invention further provides a picosecond ultrasonic system thatincorporates optical elements for delivering the probe beam to thesample, and which allows the location, shape and/or size of the probespot on the sample to be kept substantially constant and free fromchanges due to the variation of the optical path length of the probe.This is a more general case than the above-mentioned use of an opticalfiber for a similar purpose. Furthermore, “active” correction schemescan be employed in which the characteristics of the probe spot aresensed, and in which the characteristics of probe beam (e.g., profileand location) are adaptively corrected.

The invention further teaches a picosecond ultrasonic system thatincorporates an optical guiding system in which the pump and probe beamsare focused separately onto the sample. The pump and probe beams may bescanned laterally relative to each other. In particular, a guiding andfocusing system can be employed in which the probe beam is guidedthrough an optical fiber assembly with a tapered end which effects nearfield focusing into a spot which is smaller than the pump beam, andwhich may be scanned over small displacements relative while the pumpbeam is held substantially stationary. The use of a reduced tip fibermakes it possible to achieve spots for the pump and probe withdimensions as small as 1000 Å.

It is thus possible to investigate the properties of a sample throughthe study of waves propagating across the surface from one point toanother. A second purpose is to generate bulk waves which travel throughthe sample from the pumped region to the probe spot. Other applicationspertain to structures that are laterally patterned. In this case thepump light may be directed so as to be absorbed in a “dot”, i.e. a filmwhich has a very small area. Stress waves generated in this dot thenpropagate to the region of the structure that is sensed by the probepulse.

Also disclosed is a picosecond ultrasonic system in which the results ofmeasurements are compared with computer simulations of the measuredresponse or responses (1)-(5), for example. To perform the simulationthe following steps are performed. Reference is also made to the flowchart of FIG. 21.

(A) Initial Stress Distribution

The stress distribution in the sample produced as a result of theabsorption of the pump pulse is calculated using known values for theoptical absorption of the various materials present in the sample, thespecific heats of these materials, the thermal expansion coefficients,and the elastic constants. To calculate the stress distribution theeffect of thermal diffusion may be taken into account. For a samplecomposed of several planar films of different materials with materialproperties uniform throughout each film the following procedure is used.

From the optical constants and thicknesses of the films the electricfield due to the pump light pulse at all points in the structure iscalculated in terms of the amplitude, angle of incidence, andpolarization of the pump beam incident on the sample surface. Thiscalculation is most readily performed through the use of opticaltransfer matrices. Next, from the calculated electric fielddistribution, the energy absorbed in the structure as a function ofposition is calculated. Next, the effect of thermal diffusion on theabsorbed energy distribution is considered. Next, the temperature riseof each part of the sample is calculated. This temperature rise is theenergy deposited per unit volume divided by the specific heat per unitvolume. Next, the stress at all points in the sample is then calculatedfrom the temperature rise by multiplying the temperature rise by thethermal expansion coefficient and the appropriate elastic modulus.

(B) Change in Stress and Strain with Time

The change in stress and strain in the sample is next calculated as afunction of time and position using the laws of physical acoustics. Thiscalculation is effectively performed by means of a “stepping algorithm”,which performs the following computations.

First, a time step τ is chosen. For each film or layer that comprisesthe structure of interest a bin size b equal to the time τ multiplied bythe sound velocity in the film is then calculated. Each film is thendivided into bins of this size or smaller. By example, smaller size binscan be employed at any film boundary. The time step τ is chosen so thateach film preferably contains a large number of bins. The results of theforegoing give the stress set up by the pump pulse in each bin of thestructure. Next, the stress in each bin is decomposed into twocomponents, one initially propagating towards the free surface of thesample and one away from it. Within a given film these two componentsare stepped forward from bin to bin in the appropriate direction. For abin adjacent to the boundary between two films the stress propagatingtowards the boundary is stepped partly into the first bin on the otherside of the boundary and still propagating in the same direction andpartly into the original bin but propagating in the reverse direction.The fraction of the stress that is stepped across the interface and thefraction which reverses direction are calculated from the laws ofphysical acoustics. At the top (free) surface of the structure thestress in the bin adjacent to the surface and propagating towards thesurface remains in the same bin but has its direction reversed, i.e., itbecomes a stress pulse propagating into the interior of the structurerather than towards the top surface. By applying this procedure to allbins for a sufficient number of time steps τ, the stress distributioncan be calculated for as long a time as is required for comparison withthe measured results. From the calculated stress the strain iscalculated by division by the appropriate elastic coefficient.

Samples that are of interest in chip fabrication typically have a numberof thin films deposited on top of a semiconductor substrate. Presently,the total thickness of these thin films is a few microns or less,whereas the substrate is typically approximately 200 microns thick. Animportant advantage of this “stepping method” is that it is notnecessary to consider stress propagation throughout the entiresubstrate. Instead it is normally sufficient to consider just one bin ofthe substrate together with “boundary conditions”specified as follows.

(1) At each time step τ the stress within the single bin of thesubstrate and propagating towards the substrate can be considered to becompletely transferred into the remainder of the substrate so that nopart of this stress is reflected. (2) The stress within the substratebin and propagating towards the film structure is taken to be zero. Thisdescription of the treatment of the substrate holds if the amount oflight that reaches the substrate, after passing through whatever filmsare deposited onto the substrate, is negligible. This condition holdsfor the majority of structures which are of current industrial interest.

When this condition is not satisfied, and light does reach thesubstrate, it is desirable to include in the simulation a thickness ofthe substrate sufficient to include the entire depth over which the pumpor the probe light can significantly penetrate. This depth is typicallysome number, e.g. five, of absorption lengths of the pump or probelight. This region of the substrate is then divided into bins ofthickness as specified above. The last bin of the substrate is thentreated according to the following boundary conditions.

First, at each time step the stress within the last bin of thesubstrate, and propagating towards the interior of the substrate, can beconsidered to be completely transferred into the remainder of thesubstrate so that no part of this stress is reflected. Second, thestress within the last bin of the substrate, and propagating towards thefilm structure, is taken to be zero.

For some samples the above division of the simulation into theconsideration of the calculation of the temperature rise and thepropagation of the stress may not be applicable. It is noted that, assoon as energy is deposited into any part of the sample, a stress is setup and mechanical waves are launched into adjacent regions. If thediffusion of energy is sufficiently large and continues for a sufficientperiod of time then the changing temperature and associated stressdistribution in the sample will continue to generate new stress waves.However, the extension of the simulation to include this effect isstraightforward.

In some samples, particularly metal films of high electricalconductivity, a more detailed treatment of the diffusion of energy isrequired. The energy in the pump light pulse is initially input to theconduction electrons, thereby raising their energy considerably abovethe Fermi level. These electrons have a very high diffusion coefficientand may spread a significant distance through the sample before losingtheir excess energy as heat to the lattice. Under these conditions thediffusion of the energy is not adequately described by Fourier's law forclassical heat conduction. Instead it is preferred to use a moremicroscopic approach, taking into account the diffusion rate of theelectrons and the rate at which they lose energy.

(C) Calculation of the Transient Response Measured by the Probe

From the calculated strain distribution as a function of depth into thesample, the changes Δn and Δκ in the optical constants are calculated.This step requires knowledge of the derivatives of the optical constantsn and κ with respect to elastic strain.

From the calculated changes Δn and Δκ in the optical constants as afunction of depth, and the unperturbed optical constants of the films,at least one of the quantities ΔR, ΔT, ΔP, ΔΦ and ΔR is calculated andcompared with the measured results. This calculation is mostconveniently carried out through the use of optical transfer matrices.

The above description of the simulation steps A-C is presented in termsof a one-dimensional model considering only the variation of theelectric field of the probe light, the elastic stress, the elasticstrain, etc., upon the distance along the direction normal to thesurface of the sample. It is within the scope of this invention toextend the calculations to allow for the variation in the intensity ofthe pump and probe beams within the plane of the surface of the sample.This approach is useful for the calculation of the change in thepropagation angle of the reflected probe light Δβ.

A series of such simulations are performed in which the assumedthicknesses of the films in the structure are varied. By comparison ofthe results of the simulation with some or all of the measuredquantities ΔR, ΔT, ΔP, ΔΦ and Δβ the thicknesses of the films aredetermined.

It is also within the scope of this invention to adjust the filmthicknesses so as to be consistent with results of any or all of: (a)measurements of the optical reflectivity through measurements of theincident and reflected average intensity of the pump and/or probe beams;(b) measurements of the average phase change of the pump and/or probebeams upon reflection; and (c) measurements of the average polarizationand optical phase of the incident and reflected pump and/or probe beams.

It is further within the scope of the teaching of this invention toinclude simulations which incorporate as adjustable parameters at leastone of the following for one or more films in order to find a best-fitto measured data.

A first adjustable parameter is the film thickness, so as to adjust thethicknesses obtained in accordance with the method described above.

In this regard reference can be had to an article entitled“Time-resolved study of vibrations of α-Ge:H/α-Si: multilayers”,Physical Review B, vol. 38, no. 9, Sep. 15, 1988, H. T. Grahn et al.,wherein reference is made to a simulation of a multilayer structure anda variation in layer thickness (as well as sound velocities). As wasreported in this article, it was not possible to find parameters suchthat the simulated response was in agreement with an experimentallyobserved ΔR(t). Reference may also be had, by example, to the followingarticles that were also coauthored by one of the inventors of thispatent application: “Sound velocity and index of refraction of AlAsmeasured by picosecond ultrasonics”, Appl. Phys. Lett. 53 (21), Nov. 21,1988, pp. 2023-2024, H. T. Grahn et al.; “Elastic properties of siliconoxynitride films determined by picosecond acoustics”, Appl. Phys. Lett.53 (23), Dec. 5, 1988, pp. 2281-2283, H. T. Grahn et al.; and “Study ofvibrational modes of gold nanostructures by picosecond ultrasonics”,Appl. Phys. 73 (1), Jan. 1, 1993, pp. 37-45, H. N. Lin et al.

A second adjustable parameter is the sound velocity. An example of asituation in which one may determine the sound velocity has beendescribed above. Thus, in this context what is taught is thedetermination of the parameters n, d, and v by comparison of themeasured data with simulations, rather than by a measurement of thefrequency f(θ) as a function of the angle θ.

A third adjustable parameter is the crystal orientation in a film. Thiscan be achieved through measurement of the sound velocity, which isdependent on crystal orientation in all crystals, even those with cubicsymmetry. In non-cubic crystals the crystal orientation of the film, orthe preferential orientation of crystalline grains, leads to anisotropicoptical properties which can be detected via the measurements of theabove described optical measures of the optical reflectivity bydetermining the incident and reflected average intensity of the pumpand/or probe beams; the average phase change of the pump and/or probebeams upon reflection; and/or the average polarization and optical phaseof the incident and reflected pump and/or probe beams.

A fourth adjustable parameter is interface roughness. By example, theinterface roughness parameter causes a broadening of a stress pulsewhich is transmitted across, or reflected at, the interface.

A fifth adjustable parameter is the interface adhesion strength, as willbe described in further detail below.

A sixth adjustable parameter is the static stress. One suitableprocedure by which this can be determined has been described previouslyin the context of measurements made at two or more temperatures of thesample.

A seventh adjustable parameter is the thermal diffusivity. The thermaldiffusivity of the different films in the sample affects the shape andmagnitude of the generated stress pulses. By treating the thermaldiffusivity as an adjustable parameter, and selecting it to give thebest agreement between the simulation and the measured data, the thermaldiffusivity of a particular film in the structure can be determined.

An eighth adjustable parameter is the electronic diffusivity. In somesamples which contain metal films with high electrical conductivity thediffusion of the conduction electrons before they lose the energy thatthey have received from the pump pulse has a large effect on the shapeand magnitude of the stress pulses which are generated. By treating theelectronic diffusivity as an adjustable parameter, and adjusting it togive the best agreement between the simulation and the measured data,the electronic diffusivity of a particular film in the structure can bedetermined.

It should be appreciated that the seventh and eight adjustableparameters provide, separately or in conjunction with one another, ameans for the determination of the electrical resistance of metallicfilms.

A ninth adjustable parameter involves the optical constants of thefilm(s) and/or substrate.

A tenth, related adjustable parameter is the derivatives of the opticalconstants with respect to stress or strain.

An eleventh adjustable parameter is the surface roughness. The surfaceroughness has the consequence that a stress pulse reflected at thesurface of a sample is broadened. This broadening may be introduced intothe simulation and adjusted until the simulation gives the bestagreement with the measured data. In this way the surface roughness canbe determined.

A twelfth adjustable parameter is interfacial contamination. If aninterface between two materials A and B is contaminated by the presenceof a thin layer of another material C, the presence of the layer Caffects the reflection and transmission coefficients for stress wavesincident on the interface. For two elastic media in perfect mechanicalcontact the reflection and transmission coefficients are given bywell-known formulas from physical acoustics. The effect of interfaceadhesion strength on the coefficients is discussed below. Thecoefficients may also be affected by other effects which are unrelatedto adhesion strength. For example, in addition to changing the strengthof the coupling between A and B (i.e., the adhesion strength) thecontamination layer C provides a layer of mass at the interface whichaffects the acoustic propagation. The contamination layer C may alsolead to additional optical absorption at the interface. The additionaloptical absorption of the pump pulse will in this case result inadditional stress waves to be generated at the interface. The detectionof these additional stress waves provides a means for detecting thepresence of the contamination layer C. This method can be applied toadvantage for detecting contamination on the surface of opticallytransparent bulk materials.

A thirteenth adjustable parameter is related to dimensions other thanthickness and geometrical shape. These parameters are generally notrelevant to measurements on samples consisting solely of planar films.Instead, these adjustable parameters enter into the characterization ofsamples of the type mentioned above with respect to laterally patternedstructures and the like. These adjustable parameters apply as well tothe characterization of an array of identical structures havingdimensions much less than the pump and probe spot diameter, as describedbelow.

A further adjustable parameter relates to the presence of and thicknessof a region of intermixing between two adjacent layers.

An important aspect of this invention concerns the precise relationbetween the computer simulations and the transient optical responsesmeasured by the system. The following discussion describes the essentialaspects of this relation for the particular example of a samplecontaining a number of planar films whose lateral extent is much greaterthan their thickness, and also greater than the linear dimensions of theregion of the sample illuminated by the pump and probe pulses. Ageneralization of this discussion to laterally patterned structures willbe evident to workers skilled in the relevant art, when guided by thefollowing teachings. Similarly, the following discussion will consider,again as a specific example, a particular one of the transient opticalresponses, namely the change ΔR(t) in optical reflectivity. Thegeneralization of the discussion to a consideration of the othertransient optical responses aforementioned should also become evident toworkers skilled in the relevant art, when guided by the followingteachings.

In this example the computer simulations calculate the change in theoptical reflectivity ΔR_(sim)(t) of the sample when it is illuminatedwith a pump pulse of unit energy per unit area of the sample. Thesimulation also gives a value for the static reflection coefficient ofthe pump and probe beams. The system measures the transient changeΔP_(probe-refl) in the power of the reflected probe pulse as determined,for example, by photodiode D1 in FIG. 18. It also measures the staticreflection coefficients of the pump and probe beams from a ratio of thepower in the incident and reflected beams. The incident probe power ismeasured by photodiode D2 in FIG. 18, the reflected probe power ismeasured by D1, the incident pump power is measured by D4, and thereflected pump power is measured by D3.

To relate the simulation results for the transient change in the opticalreflectivity to the system measurement it is necessary to know: (a) thepower of the pump and probe beams; (b) the intensity profiles of thesebeams; and (c) their overlap on the sample surface.

Let us suppose first that the pump beam is incident over an areaA_(pump) and that within this area the pump intensity is uniform. Thenfor each applied pump pulse the pump energy absorbed per unit area is$\begin{matrix}{\frac{P_{{pump}\text{-}{inc}}}{A_{pump}}\frac{( {1 - R_{pump}} )}{f}} & (3)\end{matrix}$

where f is the repetition rate of the pump pulse train, and R_(pump) isthe reflection coefficient for the pump beam. Thus, the change inoptical reflectivity of the each probe light pulse will be$\begin{matrix}{{\Delta \quad {R_{sim}(t)}\frac{P_{{pump}\text{-}{inc}}}{A_{pump}}}\frac{( {1 - R_{pump}} )}{f}} & (4)\end{matrix}$

and the change in power of the reflected probe beam will be$\begin{matrix}{{{\Delta \quad P_{{probe}\text{-}{ref1}}} = {P_{{probe}\text{-}{inc}}\Delta \quad {R_{sim}(t)}\frac{P_{{pump}\text{-}{inc}}}{A_{pump}}}}\frac{( {1 - R_{pump}} )}{f}} & (5)\end{matrix}$

In a practical system the illumination of the sample does not, in fact,produce a uniform intensity of the incident pump beam. Moreover, theintensity of the probe light will also vary with position on the samplesurface. To account for these variations the equation forΔP_(probe-refl) is modified to read $\begin{matrix}{{{\Delta \quad P_{{probe}\text{-}{ref1}}} = {P_{{probe}\quad \text{-}{inc}}\Delta \quad {R_{sim}(t)}\frac{P_{{pump}\text{-}{inc}}}{A_{effective}}}}\frac{( {1 - R_{pump}} )}{f}} & (6)\end{matrix}$

where the effective area A_(effective) is defined by the relation

where I_(probe-inc) ({right arrow over (_(r)+L )}) and I_(pump-inc)({right arrow over (_(r)+L )}) are respectively the $\begin{matrix}{A_{effective} = \frac{\int{{I_{{pump}\text{-}{inc}}( \overset{harpoonup}{r} )}{A}{\int{{I_{{probe}\text{-}{inc}}( \overset{harpoonup}{r} )}{A}}}}}{\int{{I_{{pump}\text{-}{inc}}( \overset{harpoonup}{r} )}{I_{{probe}\text{-}{inc}}( \overset{harpoonup}{r} )}( {A} }}} & (7)\end{matrix}$

intensities of the probe and pump beams on the surface of the sample.One can consider A_(effective) to be an effective area of overlap of thepump and probe beams.

Analogous expressions can be derived for the change in opticaltransmission ΔT(t), the change in optical phase ΔΦ(t), the change inpolarization ΔP(t), and the change Δβ(t) in the angle of reflection ofthe probe light.

The following quantities are measured by the system: ΔP_(probe-refl),P_(probe-inc), P_(pump-inc), R_(pump), R_(probe). The computersimulation gives predicted values for AR_(sim)(t), R_(pump), andR_(probe). Thus the following comparisons can be made between thesimulation and the system measurements in order to determine thecharacteristics of the sample.

(1) A comparison of the simulated and measured reflection coefficientR_(pump).

(2) A comparison of the simulated and measured reflection coefficientR_(probe).

(3) A comparison of the simulated and measured transient changeΔP_(probe-refl) in the power of the reflected probe light.

To make a comparison of the simulated and measured change, it can beseen from the preceding equation (6) that it is necessary to know thevalue of A_(effective). This can be accomplished by one or more of thefollowing methods.

(a) A first method directly measures the intensity variations of thepump and probe beams over the surface of the sample, i.e, I_(probe-inc)({right arrow over (_(r)+L )}) and I_(pump-inc) ({right arrow over(_(r)+L )}) as a function of position, and uses the results of thesemeasurements to calculate A_(effective). This is possible to accomplishbut requires very careful measurements which may be difficult toaccomplish in industrial environment.

(b) A second method measures the transient response ΔP_(probe-refl) fora sample on a system S for which the area A_(effective) is known. Thismethod then measures the response ΔP_(probe-refl) of the same sample onthe system S′ for which A_(effective) is to be determined. The ratio ofthe responses on the two systems gives the inverse of the ratio of theeffective areas for the two systems. This can be an effective methodbecause the system S can be chosen to be a specially constructed systemin which the areas illuminated by the pump and probe beams are largerthan would be desirable for an instrument with rapid measurementcapability. Since the areas are large for this system it is simpler tomeasure the intensity variations of the pump and probe beams over thesurface of the sample, i.e, I_(probe-inc) ({right arrow over (_(r)+L )})and I_(pump-inc) ({right arrow over (_(r)+L )}) as a function ofposition. This method is effective even if the quantities which enterinto the calculation of the simulated reflectivity change ΔR_(sim)(t)are not known.

(c) A third method measures the transient response ΔP_(probe-refl) for asample in which all of the quantities are known which enter into thecalculation of the simulated reflectivity change ΔR_(sim)(t) of thesample when it is illuminated with a pump pulse of unit energy per unitarea of the sample. Then by comparison of the measured transientresponse ΔP_(probe-refl) with the response predicted from the Eq. 6 theeffective area A_(effective) is determined.

To build a truly effective instrument it is essential that the effectivearea A_(effective) be stable throughout the course of a sequence ofmeasurements. To ensure this, the system of this invention incorporatesmeans for automatically focusing the pump and probe beams onto thesurface of the sample so as to achieve a reproducible intensityvariation of the two beams during every measurement. The automaticfocusing system provides a mechanism for maintaining the system in apreviously determined state in which the size and relative positions ofthe beams on the sample surface are appropriate for effective transientresponse measurements.

It should be noted that for any application in which the amplitude of anoptical transient response is used to draw quantitative conclusionsabout a sample (for example, when the magnitude of a feature that arisesfrom an acoustic echo is influenced by the condition of a buriedinterface) a calibration scheme such as described above must be afeature of the measurement system.

The preceding description of the method for the comparison of thecomputer simulation results and the system measurements supposes thatthe several detectors in the measurement system are calibrated. It iscontemplated that such a system will use detectors operating in thelinear range so that the output voltage V of each detector isproportional to the incident optical power P. For each detector there isthus a constant G such that V=GP. The preceding description assumes thatthe constant G is known for each and every detector. In the case thatthis information is not available, the individual calibration factorsassociated with each of the individual detectors measuringP_(probe-inc), P_(pump-inc), and P_(probe-refl) may be combined withA_(effective) and f into a single overall system calibration constant C.Therefore in terms of a calibration factor C, Eq. 6 could be expressedas

ΔV _(prob-refl) =C V _(probe-inc) ΔR _(sim)(t)V _(pump-inc)(1−R_(pump))  (8)

where ΔV_(probe-refl) is the output voltage from detector used tomeasure the change in the power of the reflected probe light (D1),V_(pump-inc) is the output voltage from the detector used to measure theincident pump light (D4), and V_(probe-inc) is the output voltage of thedetector used to measure the incident probe light (D2). Thus, to providean effective instrument it is sufficient to determine the constant C.This can be accomplished by either of the following two methods.

(a) A first method measures the transient response ΔV_(probe-refl) for asample in which all of the quantities are known which enter into thecalculation of the simulated reflectivity change ΔR_(sim)(t) of thesample when it is illuminated with a pump pulse of unit energy per unitarea of the sample. Next, the method measures V_(probe-inc) andV_(probe-inc) then determines R either by measurement or from thecomputer simulation. The method then finds the value of the constant Csuch that Eq. 8 is satisfied.

(b) A second method measures the transient response ΔV_(probe-refl) fora reference sample for which the transient optical response ΔR(t), whenit is illuminated with a pump pulse of unit energy per unit area of thesample, has been measured using a system which has been previouslycalibrated, for example, by one or more of the methods described above.The method then measure V_(probe-inc) and V_(pump-inc)., determinesR_(pump) by measurement, and then finds the value of the constant C suchthat the following equation is satisfied.

ΔV _(probe-refl) =C V _(probe-inc) ΔR(t)V _(pump-inc)(1−R)  (9)

For both of these methods it is important to establish the autofocusconditions prior to making measurements of ΔV_(prob-refl) since Cdepends on the value of A_(effective).

The teaching of this invention furthermore encompasses a picosecondultrasonic system in which the results of measurements are compared withcomputer simulations of the measured response, as described above, butusing a different method to perform the simulation. In this case thefollowing steps may be employed.

First, the initial stress distribution in the structure is calculatedusing the method described above.

Second, the acoustical normal modes of the structure are calculatedthrough solution of the equations of physical acoustics together withappropriate boundary conditions at the interfaces between the films, atthe free surface of the sample, and at the free surface of thesubstrate. All normal modes up to certain maximum frequency f_(max) arecalculated. The choice of this maximum frequency is related to thesharpness of the features, such as echoes, that appear in the measureddata. As an approximate rule, if it is desired to simulate data for astructure of interest which has a characteristic time-scale τ, it isnecessary to choose f_(max) such that the product of f_(max) and τ is atleast as large as unity. Thus, for example, if the measured datacontains an echo of width 1 psec, then to perform an accurate simulationit is desirable to calculate all normal modes up to the frequency 1000GHz.

The substrate thickness is typically in the range around 200 microns,whereas often the total thickness of the thin films deposited onto thesubstrate is a micron or even less. A calculation of the normal modes ofa sample consisting of films on a substrate of this thickness is verydifficult and time-consuming because of the very large number ofacoustic modes with very closely-spaced frequencies. However, for thepurposes of creating an accurate simulation of the typical data on thistype of sample it is not necessary to use the actual thickness of thesubstrate. Instead it is sufficient to consider the “substrate” to havea thickness much less than the real physical substrate. The thickness ofthis artificial substrate should be sufficiently large such that thetime required for an acoustic wave to propagate through the substratefrom the thin films deposited on the front surface of the substrate tothe far side of the substrate and back again is longer than the totaltime span over which the data to be simulated extends. Thus, forexample, if the data extends from zero time delay of the probe relativeto the pump to a time delay of 1000 psecs, and the sound velocity v inthe substrate is 5×10⁵ cm sec⁻¹, then the artificial substrate can betaken to have a thickness of as little as 2.5 microns. If the thicknessis at least this great no acoustic echoes can return from the back ofthe substrate during the time that measurements are made, and hence thedifference in thickness between the artificial substrate and the actualsubstrate is irrelevant.

Third, the initial stress distribution produced by the pump beam isdecomposed into a sum over the normal modes just calculated. It ispossible to choose a set of amplitudes for the normal modes such thatwhen the contributions of each normal mode are added together, takingallowance for the amplitude of each mode, the initial stressdistribution is accurately reproduced. The initial amplitude of the nthnormal mode may be denoted as A_(n).

Fourth, each normal mode has a characteristic spatial stress patternassociated with it This stress pattern gives a change in the reflectioncoefficient of the probe light which can be calculated according to themethods described above. Let this change when the nth mode has unitamplitude be B_(n). This change is linear in the amplitude of theacoustic normal mode. Hence, the total change in the reflectivity of theprobe light at time zero is

ΔR(t=0)=sum_(n) A _(n) B _(n).  (10)

Fifth, let the frequency of the nth normal mode be f_(n). Then the totalchange in reflectivity of the probe light at any later time t can becalculated as

ΔR(t)=sum_(n) A _(n) B _(n) cos (2πf _(n) t).  (11)

This simulation method has the advantage that through the use of theformula just given the change in reflectivity at any chosen time, orwithin any chosen time range, may be calculated without the need toconsider the acoustic or optical processes occurring in the sample forall times intermediate between the application of the pump pulse and thetime of interest. It is important to note that the amplitudes A_(n) andthe coefficients B_(n) need be calculated only once, and can then beused to find the response at any later time.

It should be further noted that the above description refers to the useof this method for the calculation of the change in reflected intensityof the probe beam. However, completely analogous methods can be used tosimulate the other responses of interest, i.e. ΔT, ΔP, ΔΦ, and Δβ.

As was indicated previously, the teaching of this invention is alsodirected to a picosecond ultrasonic system which enables the measurementof a vibrational response of a sample that includes, by example, a verythin film on a substrate, or a very thin film on a significantly thickerfilm. By example, a substrate may have a layer of a metal, such asaluminum, and an intervening layer comprised of a polymer. The measuredresponse is then analyzed to determine the damping rate of the thicknessvibration of the film. This damping rate is compared with a damping ratedetermined for a model based on classical acoustics in which theinterface between the thin film and the substrate (or thicker film) ischaracterized by a coupling parameter (“adhesion strength”) per unitarea. This coupling parameter, which may be considered to be a springconstant parameter that is a linear property per unit area, is thestrength, of a spring per unit area which connects the surface of thethin film to the substrate, or to the thicker film. The adhesionstrength is adjusted to give agreement between the simulation and themeasured value of the damping, and is thus used as a measure of thequality of the interface.

As was also indicated previously, the teaching of this inventionfurthermore pertains to a picosecond ultrasonic system in which a sampleis comprised of an array of identical structures having dimensions muchless than the pump and probe spot diameter. In this case each structureis simultaneously excited by the pump beam and then simultaneouslyexamined by the probe beam. The response of each structure is simulatedby the methods described above. The characteristics of the structuresare then deduced by comparison of the simulation and the measuredresponse.

Relatedly, this invention also teaches methods for deducing thedimensions of substantially identical patterned structures arrangedperiodically, and for deducing the statistical distribution of sizes ofsuch structures. This is accomplished by comparing the observed responseof the structures, to a stress pulse that is induced by the pump pulse,to simulations of the array of vibrating structures.

Further in this regard, the teaching of this invention also pertains tomethods for deducing the physical characteristics of thin filmspatterned mechanically or by lithographic means into structures. Stepsof the method include simulation of the mechanical vibrations of asingle structure, calculation of the change in the probe beam after itimpinges on the structure, and adjusting the physical characteristics ofthe simulated structure and interfaces in order to obtain a best fit tothe observed response.

Further in accordance with the teaching of this invention, a picosecondultrasonic system employs a method for deducing the physicalcharacteristics of a sample, and uses an analysis of an acoustic echo orechoes based on either or both of the following two methods.

In a first method a characterization of the time of arrival of an echois obtained by means of the location in time of one or more echofeatures, such as a point of maximum or minimum amplitude or inflectionpoint.

In a second method a characterization of the time of arrival of the echoas seen in ΔR(t) (or, by example, ΔT(t), ΔP(t), ΔΦ(t), and Δβ(t)) byconvolution of the measured echo with a suitably chosen function f(t) ofthe time. Thus, the convolution

C(t ₁)=∫ΔR(t)f(t−t ₁)dt  (12)

is calculated. The time t₁ is then adjusted so as to maximize the resultof the convolution, i.e. to maximize C. The resulting value of t₁ isthen used as an estimate of the arrival time of the echo. The functionf(t) may be the shape of the echo measured on a reference sample havingknown physical characteristics or determined by simulation. The echotime, or times, as determined are then used to yield film thicknesses orinterface characteristics.

In view of the foregoing descriptions, it should thus be realized thatthe teaching of this invention also pertains to methods for deducing thephysical characteristics of thin films or interfaces, in which the stepsinclude the sequential application of some or all of the above-describedmethods in order to determine the physical parameters of a complexsample having more than one layer or interface.

The teaching of this invention also pertains to methods for deducing thesound velocity and refractive index of a film or substrate in which astress wave is generated by a light pulse, and in which an oscillatingresponse is observed in the detected probe beam as a function of delay,and measurements of the oscillation period are made corresponding to atleast two angles of incidence of the probe beam on the sample's surface.Measurements at several angles may be made sequentially orsimultaneously. In this case the film may be partially absorbing, andcould be a film which is underneath (i.e, on the substrate side of)another partially-absorbing film or films.

Also encompassed by the teachings of this invention are methods ofrelating the quality of a sample to another reference sample preparedunder a particular set of conditions, by comparing the observed temporalresponse of the sample with that measured for the reference sample undersimilar conditions. The result of the comparison may or may not ascribea cause for any observed differences to a specific physical or chemicalproperty of either sample.

The quality is considered a factor which relates the similarity ordissimilarity of the optical responses of the several samples to thegeneration of a stress wave or pulse by the pump beam.

This invention also pertains to the application of the pump and/or probebeams at different spatial locations on the sample with the intention ofcharacterizing an intervening part of sample. The intervening part ofthe sample may be, by example, an interface, a crack, or a material inwhich signals cannot be directly generated, but which is desired tocharacterize.

The teaching of this invention furthermore pertains to methods andapparatus for exciting modes of one or two dimensional patterned objectsfor the purpose of characterizing their shapes, layer thickness,adhesion, and structural integrity. This aspect of the invention may beconsidered as a generalization of the foregoing features and advantages,and is directed to samples which are not thin films of uniform thicknessand which may be large compared to their thickness. For these samplesthe analysis preferably includes the calculation of the stress, strain,electric fields due to the pump and probe light pulses, etc., as afunction of two or three spatial coordinates rather than only thedistance from the surface of the sample. While the time-step methoddescribed above may not be applicable to solving this problem, becauseit is applicable to one dimension, other numerical simulation methodsmay be applied to perform the calculation of how the stress changes withtime. Also, the previously described simulations employ optical transfermatrices to calculate the electric field distribution of the pump lightand the change in optical reflectivity (or other changes in thecharacteristics) of the probe light. However, the optical transfermatrix method is not applicable to patterned structures because, again,it is essentially a one dimensional method. Thus, another more suitablenumerical method is used instead.

The teaching of this invention also includes methods and apparatus forexciting stress pulses in one part of a thin film or multilayer in orderto detect a change in another part of the thin film, such as a presenceof a chemical reaction, intermixing, or alloying at one or moreinterfaces within the sample.

Relatedly, the teaching of this invention also encompasses thecharacterization of interfacial chemical reactions between two or morelayers, or between a layer and interface, and the correlation of theacoustical and optical measurements with reactant species. This includesthe characterization of the structural phase, and one or more of thethickness and sound velocity of the layers in the sample, including anynew layers formed by the chemical reaction.

The teachings of this invention also pertain to the characterization ofion implant dose, energy, species, or any other ion implant parametersfor an ion implant made through a film for the purpose of, by example,altering its adhesion to a substrate or an underlying layer. Thischaracterization is carried out in accordance with any of theabove-described techniques, in which the adhesion may be deduced fromthe temporal characteristics of the observed probe response, or by asimple comparison with a reference response for a sample prepared underlike conditions.

Finally, this invention teaches a method for deducing the derivative ofthe index of refraction n or extinction coefficient κ of a material withrespect to stress or strain by making measurements of the reflectivitychange in the material caused by a stress pulse, of which a computablefraction has also been detected in a second material whose derivativesof index of refraction and extinction coefficient with respect to stressor strain are known or may be determined separately.

It should thus be apparent that while the invention has beenparticularly shown and described with respect to a number of embodimentsthereof, the teachings of this invention are not to be construed to belimited to only these disclosed embodiments. That is, changes in formand details may be made to these disclosed embodiments without departingfrom the scope and spirit of the invention. The teaching of thisinvention should thus be afforded a scope that is commensurate with thescope of the claims which follow.

What is claimed is:
 1. A method for characterizing a structure,comprising the steps of: applying first electromagnetic radiation to thestructure for creating propagating stress pulses within the structure;applying second electromagnetic radiation to the structure at apredetermined incidence angle so as to intercept the propagating stresspulses; sensing a reflection or transmission of the secondelectromagnetic radiation from the structure; associating a change inthe reflection of the second electromagnetic radiation over time with avalue of an optical characteristic of the structure for determining atransient response of the structure; determining an index of refractionof the structure using an ellipsometric technique; and determining avelocity of sound in the structure in accordance with the predeterminedangle and the determined transient response and index of refraction. 2.The method of claim 1, wherein the phase of said second electromagneticradiation is varied continuously.
 3. The method of claim 1, wherein saidsecond electromagnetic radiation is pulsed.
 4. The method of claim 1,wherein said step of determining an index of refraction employs acontinuous wave laser.
 5. The method of claim 4, wherein said continuouswave laser is a HeNe laser.
 6. The method of claim 1, wherein said firstelectromagnetic radiation has substantially one half the wavelength ofsaid second electromagnetic radiation.
 7. An apparatus forcharacterizing a structure, comprising: a source of firstelectromagnetic radiation and means for applying said firstelectromagnetic radiation to the structure for creating propagatingstress pulses within the structure; a source of second electromagneticand means for applying said second electromagnetic radiation to thestructure at a predetermined incidence angle so as to intercept thepropagating stress pulses; a sensor for sensing a reflection ortransmission of the second electromagnetic radiation from the structure;and a processor for associating a change in the reflection of the secondelectromagnetic radiation over time with a value of an opticalcharacteristic of the structure for determining a transient response ofthe structure; said processor further determining an index of refractionof the structure using an ellipsometric technique and determining avelocity of sound in the structure in accordance with the predeterminedangle and the determined transient response and index of refraction. 8.The apparatus of claim 7, wherein the phase of said secondelectromagnetic radiation is varied continuously.
 9. The apparatus ofclaim 7, wherein said second electromagnetic radiation is pulsed. 10.The apparatus of claim 7, wherein said processor employs a continuouswave laser to determine said index of refraction.
 11. The apparatus ofclaim 10, wherein said continuous wave laser is a HeNe laser.
 12. Theapparatus of claim 7, wherein said first electromagnetic radiation hassubstantially one half the wavelength of said second electromagneticradiation.